8.10: Difference between revisions

Latest revision as of 11:18, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
8.10.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} \leq 1} `x^{1-a}e^{x}\incGamma@{a}{x} \leq 1`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, 0 < a, a \leq 1}	(x)^(1 - a)* exp(x)*GAMMA(a, x) <= 1	(x)^(1 - a)* Exp[x]*Gamma[a, x] <= 1	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
8.10.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})} `\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, 0 < a, a \leq 1, \realpart@@{a} > 0}	GAMMA(a)-GAMMA(a, x) >= ((x)^(a - 1))/(a)*(1 - exp(- x))	Gamma[a, 0, x] >= Divide[(x)^(a - 1),a]*(1 - Exp[- x])	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
8.10.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta} `x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(x)^(1 - a)* exp(x)GAMMA(a, x) = 1 +(a - 1)/(x)vartheta	(x)^(1 - a)* Exp[x]Gamma[a, x] == 1 +Divide[a - 1,x]\[CurlyTheta]	Failure	Failure	Failed [180 / 180] Result: .8735840245+.8333333335I Test Values: {a = -1.5, x = 1.5, vartheta = 1/23^(1/2)+1/2I} Result: -1.403124983+1.443375674I Test Values: {a = -1.5, x = 1.5, vartheta = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [180 / 180] Result: Complex[0.8735840235649492, 0.8333333333333331] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.4031249827424481, 1.4433756729740643] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϑ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.10.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \vartheta} `0 < \vartheta`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, a \leq 2}	0 < vartheta	0 < \[CurlyTheta]	Skipped - no semantic math	Skipped - no semantic math	-	-
8.10.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}} `A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, a < 1}	A[n](<)(x)^(1 - a) exp(x)*GAMMA(a, x)	Subscript[A, n][<](x)^(1 - a) Exp[x]*Gamma[a, x]	Failure	Failure	Failed [75 / 300] Result: 1.5 < .4302083505 Test Values: {a = -1.5, x = 1.5, A[n] = 1.5, n = 1} Result: 1.5 < .4302083505 Test Values: {a = -1.5, x = 1.5, A[n] = 1.5, n = 2} ... skip entries to safe data	Failed [195 / 300] Result: Less[Complex[0.8660254037844387, 0.49999999999999994], 0.43020835059088497] Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[Complex[0.8660254037844387, 0.49999999999999994], 0.43020835059088497] Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
8.10.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}} `x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, a < 1}	(x)^(1 - a)* exp(x)*GAMMA(a, x) < B[n]	(x)^(1 - a)* Exp[x]*Gamma[a, x] < Subscript[B, n]	Failure	Failure	Failed [105 / 300] Result: .4302083505 < -1.5 Test Values: {a = -1.5, x = 1.5, B[n] = -1.5, n = 1} Result: .4302083505 < -1.5 Test Values: {a = -1.5, x = 1.5, B[n] = -1.5, n = 2} ... skip entries to safe data	Failed [225 / 300] Result: Less[0.43020835059088497, Complex[0.8660254037844387, 0.49999999999999994]] Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[0.43020835059088497, Complex[0.8660254037844387, 0.49999999999999994]] Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
8.10#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1} = \frac{x}{x+1-a}} `A_{1} = \frac{x}{x+1-a}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	A[1] = (x)/(x + 1 - a)	Subscript[A, 1] == Divide[x,x + 1 - a]	Skipped - no semantic math	Skipped - no semantic math	-	-
8.10#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1} = \frac{x+1}{x+2-a}} `B_{1} = \frac{x+1}{x+2-a}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	B[1] = (x + 1)/(x + 2 - a)	Subscript[B, 1] == Divide[x + 1,x + 2 - a]	Skipped - no semantic math	Skipped - no semantic math	-	-
8.10#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}} `A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	A[2] = (x(x + 3 - a))/((x)^(2)+ 2(2 - a)x +(1 - a)(2 - a))	Subscript[A, 2] == Divide[x(x + 3 - a),(x)^(2)+ 2(2 - a)x +(1 - a)(2 - a)]	Skipped - no semantic math	Skipped - no semantic math	-	-
8.10#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}} `B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	B[2] = ((x)^(2)+(5 - a)x + 2)/((x)^(2)+ 2(3 - a)x +(2 - a)(3 - a))	Subscript[B, 2] == Divide[(x)^(2)+(5 - a)x + 2,(x)^(2)+ 2(3 - a)x +(2 - a)(3 - a)]	Skipped - no semantic math	Skipped - no semantic math	-	-
8.10.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}} `I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{a} > 0}	I = int((t)^(a - 1)* exp(t), t = 0..x)	I == Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}, GenerateConditions->None]	Failure	Failure	Failed [90 / 90] Result: -2.374226751+.5000000000I Test Values: {I = 1/23^(1/2)+1/2I, a = 1.5, x = 1.5} Result: .5451660792+.5000000000I Test Values: {I = 1/23^(1/2)+1/2I, a = 1.5, x = .5} ... skip entries to safe data	Failed [27 / 27] Result: Complex[-2.240252154794788, -4.0113152157384396^-17] Test Values: {Rule[Complex[0, 1], 1], Rule[a, 1.5], Rule[x, 1.5]} Result: Complex[-1.240252154794788, -4.0113152157384396^-17] Test Values: {Rule[Complex[0, 1], 2], Rule[a, 1.5], Rule[x, 1.5]} ... skip entries to safe data
8.10.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}} `\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{a} > 0}	int((t)^(a - 1)* exp(t), t = 0..x) = GAMMA(a)(x)^(a) (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a)	Error	Failure	Missing Macro Error	Successful [Tested: 9]	Skip - symbolical successful subtest
8.10.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I} `\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, a \geq 0}	((a + 1)(a + 2)- x)/((a + 1)(a + 2 + x)) < a(x)^(- a) exp(- x)*I	Divide[(a + 1)(a + 2)- x,(a + 1)(a + 2 + x)] < a(x)^(- a) Exp[- x]*I	Skipped - no semantic math	Skipped - no semantic math	-	-
8.10#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}} `c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1+a)} > 0}	c[a] = (GAMMA(1 + a))^(1/(a - 1))	Subscript[c, a] == (Gamma[1 + a])^(1/(a - 1))	Failure	Failure	Failed [39 / 40] Result: -.9011204630+.5000000000I Test Values: {a = 1.5, c[a] = 1/23^(1/2)+1/2I} Result: -2.267145867+.8660254040I Test Values: {a = 1.5, c[a] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [39 / 40] Result: Complex[-0.9011204638598199, 0.49999999999999994] Test Values: {Rule[a, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.2671458676442584, 0.8660254037844387] Test Values: {Rule[a, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.10#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{a} = (\EulerGamma@{1+a})^{-1/a}} `d_{a} = (\EulerGamma@{1+a})^{-1/a}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(1+a)} > 0}	d[a] = (GAMMA(1 + a))^(- 1/a)	Subscript[d, a] == (Gamma[1 + a])^(- 1/a)	Failure	Failure	Failed [40 / 40] Result: .388914161e-1+.5000000000I Test Values: {a = 1.5, d[a] = 1/23^(1/2)+1/2I} Result: -1.327133988+.8660254040I Test Values: {a = 1.5, d[a] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [40 / 40] Result: Complex[0.038891415918572037, 0.49999999999999994] Test Values: {Rule[a, 1.5], Rule[Subscript[d, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.3271339878658663, 0.8660254037844387] Test Values: {Rule[a, 1.5], Rule[Subscript[d, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.10.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}} `\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \geq 0, 0 < a, a < 1}	(x)/(2a)((1 +(2)/(x))^(a)- 1) < (x)^(1 - a)* exp(x)*GAMMA(a, x)	Divide[x,2a]((1 +Divide[2,x])^(a)- 1) < (x)^(1 - a)* Exp[x]*Gamma[a, x]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
8.10.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)} `x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \geq 0, 0 < a, a < 1}	(x)^(1 - a)* exp(x)GAMMA(a, x) <= (x)/(ac[a])*((1 +(c[a])/(x))^(a)- 1)	(x)^(1 - a)* Exp[x]Gamma[a, x] <= Divide[x,aSubscript[c, a]]*((1 +Divide[Subscript[c, a],x])^(a)- 1)	Failure	Failure	Failed [3 / 30] Result: .8100694499 <= .7912878480 Test Values: {a = .5, x = 1.5, c[a] = 2} Result: .6556795425 <= .6180339885 Test Values: {a = .5, x = .5, c[a] = 2} ... skip entries to safe data	Failed [18 / 30] Result: LessEqual[0.8100694501969615, Complex[0.8808481919138387, -0.05137441674828974]] Test Values: {Rule[a, 0.5], Rule[x, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[0.8100694501969615, Complex[1.0324243733930456, -0.1801654927820326]] Test Values: {Rule[a, 0.5], Rule[x, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.10.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}} `(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \geq 0, a > 0}	(1 - exp(- alpha[a]*x))^(a) <= (GAMMA(a)-GAMMA(a, x))/GAMMA(a)	(1 - Exp[- Subscript[\[Alpha], a]*x])^(a) <= GammaRegularized[a, 0, x]	Failure	Failure	Failed [78 / 270] Result: .8461432717 <= .6083748237 Test Values: {a = 1.5, alpha = 1.5, x = 1.5, alpha[a] = 1.5} Result: .9262567903 <= .6083748237 Test Values: {a = 1.5, alpha = 1.5, x = 1.5, alpha[a] = 2} ... skip entries to safe data	Failed [240 / 270] Result: LessEqual[Complex[0.7016331692747775, 0.2500919864059583], 0.608374823728911] Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[α, 1.5], Rule[Subscript[α, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[Complex[-1.369574242346028, 2.679891945423719], 0.608374823728911] Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[α, 1.5], Rule[Subscript[α, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.10.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}} `\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \geq 0, a > 0}	(GAMMA(a)-GAMMA(a, x))/GAMMA(a) <= (1 - exp(- beta[a]*x))^(a)	GammaRegularized[a, 0, x] <= (1 - Exp[- Subscript[\[Beta], a]*x])^(a)	Failure	Failure	Failed [30 / 270] Result: .6083748237 <= .3832643966 Test Values: {a = 1.5, beta = 1.5, x = 1.5, beta[a] = .5} Result: .1987480431 <= .1040340193 Test Values: {a = 1.5, beta = 1.5, x = .5, beta[a] = .5} ... skip entries to safe data	Failed [192 / 270] Result: LessEqual[0.608374823728911, Complex[0.7016331692747775, 0.2500919864059583]] Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[Subscript[β, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: LessEqual[0.608374823728911, Complex[-1.369574242346028, 2.679891945423719]] Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[Subscript[β, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.10.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}} `\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{n} > 0}	(GAMMA(n, n))/(GAMMA(n)) < (1)/(2)	Divide[Gamma[n, n],Gamma[n]] < Divide[1,2]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 1]
8.10.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}} `\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{n} > 0}	(1)/(2) < (GAMMA(n, n - 1))/(GAMMA(n))	Divide[1,2] < Divide[Gamma[n, n - 1],Gamma[n]]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 1]

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/8.10.E1 8.10.E1] || [[Item:Q2554|<math>x^{1-a}e^{x}\incGamma@{a}{x} \leq 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} \leq 1</syntaxhighlight> || <math>x > 0, 0 < a, a \leq 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) <= 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] <= 1</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/8.10.E1 8.10.E1] || <math qid="Q2554">x^{1-a}e^{x}\incGamma@{a}{x} \leq 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} \leq 1</syntaxhighlight> || <math>x > 0, 0 < a, a \leq 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) <= 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] <= 1</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/8.10.E2 8.10.E2] || [[Item:Q2555|<math>\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})</syntaxhighlight> || <math>x > 0, 0 < a, a \leq 1, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, x) >= ((x)^(a - 1))/(a)*(1 - exp(- x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, x] >= Divide[(x)^(a - 1),a]*(1 - Exp[- x])</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/8.10.E2 8.10.E2] || <math qid="Q2555">\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})</syntaxhighlight> || <math>x > 0, 0 < a, a \leq 1, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, x) >= ((x)^(a - 1))/(a)*(1 - exp(- x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, x] >= Divide[(x)^(a - 1),a]*(1 - Exp[- x])</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/8.10.E3 8.10.E3] || [[Item:Q2556|<math>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) = 1 +(a - 1)/(x)*vartheta</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] == 1 +Divide[a - 1,x]*\[CurlyTheta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8735840245+.8333333335*I
+| [https://dlmf.nist.gov/8.10.E3 8.10.E3] || <math qid="Q2556">x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) = 1 +(a - 1)/(x)*vartheta</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] == 1 +Divide[a - 1,x]*\[CurlyTheta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8735840245+.8333333335*I
 Test Values: {a = -1.5, x = 1.5, vartheta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.403124983+1.443375674*I
 Test Values: {a = -1.5, x = 1.5, vartheta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8735840235649492, 0.8333333333333331]
@@ Line 24: / Line 24: @@
 Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϑ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10.E4 8.10.E4] || [[Item:Q2557|<math>0 < \vartheta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 < \vartheta</syntaxhighlight> || <math>x > 0, a \leq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < vartheta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < \[CurlyTheta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/8.10.E4 8.10.E4] || <math qid="Q2557">0 < \vartheta</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 < \vartheta</syntaxhighlight> || <math>x > 0, a \leq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < vartheta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < \[CurlyTheta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</syntaxhighlight> || <math>x > 0, a < 1</math> || <syntaxhighlight lang=mathematica>A[n](<)*(x)^(1 - a)* exp(x)*GAMMA(a, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, n][<]*(x)^(1 - a)* Exp[x]*Gamma[a, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [75 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.5 < .4302083505
+| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || <math qid="Q2558">A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</syntaxhighlight> || <math>x > 0, a < 1</math> || <syntaxhighlight lang=mathematica>A[n](<)*(x)^(1 - a)* exp(x)*GAMMA(a, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, n][<]*(x)^(1 - a)* Exp[x]*Gamma[a, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [75 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.5 < .4302083505
 Test Values: {a = -1.5, x = 1.5, A[n] = 1.5, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.5 < .4302083505
 Test Values: {a = -1.5, x = 1.5, A[n] = 1.5, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [195 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Less[Complex[0.8660254037844387, 0.49999999999999994], 0.43020835059088497]
@@ Line 32: / Line 32: @@
 Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</syntaxhighlight> || <math>x > 0, a < 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) < B[n]</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] < Subscript[B, n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [105 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4302083505 < -1.5
+| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || <math qid="Q2558">x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</syntaxhighlight> || <math>x > 0, a < 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) < B[n]</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] < Subscript[B, n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [105 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4302083505 < -1.5
 Test Values: {a = -1.5, x = 1.5, B[n] = -1.5, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4302083505 < -1.5
 Test Values: {a = -1.5, x = 1.5, B[n] = -1.5, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [225 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Less[0.43020835059088497, Complex[0.8660254037844387, 0.49999999999999994]]
@@ Line 38: / Line 38: @@
 Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex1 8.10#Ex1] || [[Item:Q2559|<math>A_{1} = \frac{x}{x+1-a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1} = \frac{x}{x+1-a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[1] = (x)/(x + 1 - a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 1] == Divide[x,x + 1 - a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/8.10#Ex1 8.10#Ex1] || <math qid="Q2559">A_{1} = \frac{x}{x+1-a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1} = \frac{x}{x+1-a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[1] = (x)/(x + 1 - a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 1] == Divide[x,x + 1 - a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex2 8.10#Ex2] || [[Item:Q2560|<math>B_{1} = \frac{x+1}{x+2-a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1} = \frac{x+1}{x+2-a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[1] = (x + 1)/(x + 2 - a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 1] == Divide[x + 1,x + 2 - a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/8.10#Ex2 8.10#Ex2] || <math qid="Q2560">B_{1} = \frac{x+1}{x+2-a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1} = \frac{x+1}{x+2-a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[1] = (x + 1)/(x + 2 - a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 1] == Divide[x + 1,x + 2 - a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex3 8.10#Ex3] || [[Item:Q2561|<math>A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[2] = (x*(x + 3 - a))/((x)^(2)+ 2*(2 - a)*x +(1 - a)*(2 - a))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 2] == Divide[x*(x + 3 - a),(x)^(2)+ 2*(2 - a)*x +(1 - a)*(2 - a)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/8.10#Ex3 8.10#Ex3] || <math qid="Q2561">A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[2] = (x*(x + 3 - a))/((x)^(2)+ 2*(2 - a)*x +(1 - a)*(2 - a))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 2] == Divide[x*(x + 3 - a),(x)^(2)+ 2*(2 - a)*x +(1 - a)*(2 - a)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex4 8.10#Ex4] || [[Item:Q2562|<math>B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[2] = ((x)^(2)+(5 - a)*x + 2)/((x)^(2)+ 2*(3 - a)*x +(2 - a)*(3 - a))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 2] == Divide[(x)^(2)+(5 - a)*x + 2,(x)^(2)+ 2*(3 - a)*x +(2 - a)*(3 - a)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/8.10#Ex4 8.10#Ex4] || <math qid="Q2562">B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[2] = ((x)^(2)+(5 - a)*x + 2)/((x)^(2)+ 2*(3 - a)*x +(2 - a)*(3 - a))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 2] == Divide[(x)^(2)+(5 - a)*x + 2,(x)^(2)+ 2*(3 - a)*x +(2 - a)*(3 - a)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>I = int((t)^(a - 1)* exp(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>I == Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.374226751+.5000000000*I
+| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || <math qid="Q2563">I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>I = int((t)^(a - 1)* exp(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>I == Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.374226751+.5000000000*I
 Test Values: {I = 1/2*3^(1/2)+1/2*I, a = 1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5451660792+.5000000000*I
 Test Values: {I = 1/2*3^(1/2)+1/2*I, a = 1.5, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.240252154794788, -4.0113152157384396*^-17]
@@ Line 52: / Line 52: @@
 Test Values: {Rule[Complex[0, 1], 2], Rule[a, 1.5], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(a - 1)* exp(t), t = 0..x) = GAMMA(a)*(x)^(a)* (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Successful [Tested: 9] || Skip - symbolical successful subtest
+| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || <math qid="Q2563">\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(a - 1)* exp(t), t = 0..x) = GAMMA(a)*(x)^(a)* (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Successful [Tested: 9] || Skip - symbolical successful subtest
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10.E8 8.10.E8] || [[Item:Q2564|<math>\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I</syntaxhighlight> || <math>x > 0, a \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((a + 1)*(a + 2)- x)/((a + 1)*(a + 2 + x)) < a*(x)^(- a)* exp(- x)*I</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[(a + 1)*(a + 2)- x,(a + 1)*(a + 2 + x)] < a*(x)^(- a)* Exp[- x]*I</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/8.10.E8 8.10.E8] || <math qid="Q2564">\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I</syntaxhighlight> || <math>x > 0, a \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((a + 1)*(a + 2)- x)/((a + 1)*(a + 2 + x)) < a*(x)^(- a)* exp(- x)*I</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[(a + 1)*(a + 2)- x,(a + 1)*(a + 2 + x)] < a*(x)^(- a)* Exp[- x]*I</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/8.10#Ex5 8.10#Ex5] || [[Item:Q2565|<math>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</syntaxhighlight> || <math>\realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>c[a] = (GAMMA(1 + a))^(1/(a - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, a] == (Gamma[1 + a])^(1/(a - 1))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9011204630+.5000000000*I
+| [https://dlmf.nist.gov/8.10#Ex5 8.10#Ex5] || <math qid="Q2565">c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</syntaxhighlight> || <math>\realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>c[a] = (GAMMA(1 + a))^(1/(a - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, a] == (Gamma[1 + a])^(1/(a - 1))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9011204630+.5000000000*I
 Test Values: {a = 1.5, c[a] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.267145867+.8660254040*I
 Test Values: {a = 1.5, c[a] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.9011204638598199, 0.49999999999999994]
@@ Line 62: / Line 62: @@
 Test Values: {Rule[a, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10#Ex6 8.10#Ex6] || [[Item:Q2566|<math>d_{a} = (\EulerGamma@{1+a})^{-1/a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d_{a} = (\EulerGamma@{1+a})^{-1/a}</syntaxhighlight> || <math>\realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>d[a] = (GAMMA(1 + a))^(- 1/a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[d, a] == (Gamma[1 + a])^(- 1/a)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [40 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .388914161e-1+.5000000000*I
+| [https://dlmf.nist.gov/8.10#Ex6 8.10#Ex6] || <math qid="Q2566">d_{a} = (\EulerGamma@{1+a})^{-1/a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d_{a} = (\EulerGamma@{1+a})^{-1/a}</syntaxhighlight> || <math>\realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>d[a] = (GAMMA(1 + a))^(- 1/a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[d, a] == (Gamma[1 + a])^(- 1/a)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [40 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .388914161e-1+.5000000000*I
 Test Values: {a = 1.5, d[a] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.327133988+.8660254040*I
 Test Values: {a = 1.5, d[a] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [40 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.038891415918572037, 0.49999999999999994]
@@ Line 68: / Line 68: @@
 Test Values: {Rule[a, 1.5], Rule[Subscript[d, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || [[Item:Q2567|<math>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</syntaxhighlight> || <math>x \geq 0, 0 < a, a < 1</math> || <syntaxhighlight lang=mathematica>(x)/(2*a)*((1 +(2)/(x))^(a)- 1) < (x)^(1 - a)* exp(x)*GAMMA(a, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[x,2*a]*((1 +Divide[2,x])^(a)- 1) < (x)^(1 - a)* Exp[x]*Gamma[a, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || <math qid="Q2567">\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</syntaxhighlight> || <math>x \geq 0, 0 < a, a < 1</math> || <syntaxhighlight lang=mathematica>(x)/(2*a)*((1 +(2)/(x))^(a)- 1) < (x)^(1 - a)* exp(x)*GAMMA(a, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[x,2*a]*((1 +Divide[2,x])^(a)- 1) < (x)^(1 - a)* Exp[x]*Gamma[a, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || [[Item:Q2567|<math>x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)</syntaxhighlight> || <math>x \geq 0, 0 < a, a < 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) <= (x)/(a*c[a])*((1 +(c[a])/(x))^(a)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] <= Divide[x,a*Subscript[c, a]]*((1 +Divide[Subscript[c, a],x])^(a)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8100694499 <= .7912878480
+| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || <math qid="Q2567">x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)</syntaxhighlight> || <math>x \geq 0, 0 < a, a < 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) <= (x)/(a*c[a])*((1 +(c[a])/(x))^(a)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] <= Divide[x,a*Subscript[c, a]]*((1 +Divide[Subscript[c, a],x])^(a)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8100694499 <= .7912878480
 Test Values: {a = .5, x = 1.5, c[a] = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6556795425 <= .6180339885
 Test Values: {a = .5, x = .5, c[a] = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.8100694501969615, Complex[0.8808481919138387, -0.05137441674828974]]
@@ Line 76: / Line 76: @@
 Test Values: {Rule[a, 0.5], Rule[x, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10.E11 8.10.E11] || [[Item:Q2568|<math>(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}</syntaxhighlight> || <math>x \geq 0, a > 0</math> || <syntaxhighlight lang=mathematica>(1 - exp(- alpha[a]*x))^(a) <= (GAMMA(a)-GAMMA(a, x))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 - Exp[- Subscript[\[Alpha], a]*x])^(a) <= GammaRegularized[a, 0, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [78 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8461432717 <= .6083748237
+| [https://dlmf.nist.gov/8.10.E11 8.10.E11] || <math qid="Q2568">(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}</syntaxhighlight> || <math>x \geq 0, a > 0</math> || <syntaxhighlight lang=mathematica>(1 - exp(- alpha[a]*x))^(a) <= (GAMMA(a)-GAMMA(a, x))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 - Exp[- Subscript[\[Alpha], a]*x])^(a) <= GammaRegularized[a, 0, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [78 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8461432717 <= .6083748237
 Test Values: {a = 1.5, alpha = 1.5, x = 1.5, alpha[a] = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9262567903 <= .6083748237
 Test Values: {a = 1.5, alpha = 1.5, x = 1.5, alpha[a] = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.7016331692747775, 0.2500919864059583], 0.608374823728911]
@@ Line 82: / Line 82: @@
 Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[α, 1.5], Rule[Subscript[α, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10.E11 8.10.E11] || [[Item:Q2568|<math>\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}</syntaxhighlight> || <math>x \geq 0, a > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a)-GAMMA(a, x))/GAMMA(a) <= (1 - exp(- beta[a]*x))^(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, 0, x] <= (1 - Exp[- Subscript[\[Beta], a]*x])^(a)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6083748237 <= .3832643966
+| [https://dlmf.nist.gov/8.10.E11 8.10.E11] || <math qid="Q2568">\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}</syntaxhighlight> || <math>x \geq 0, a > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a)-GAMMA(a, x))/GAMMA(a) <= (1 - exp(- beta[a]*x))^(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, 0, x] <= (1 - Exp[- Subscript[\[Beta], a]*x])^(a)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6083748237 <= .3832643966
 Test Values: {a = 1.5, beta = 1.5, x = 1.5, beta[a] = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1987480431 <= .1040340193
 Test Values: {a = 1.5, beta = 1.5, x = .5, beta[a] = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [192 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.608374823728911, Complex[0.7016331692747775, 0.2500919864059583]]
@@ Line 88: / Line 88: @@
 Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[Subscript[β, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/8.10.E13 8.10.E13] || [[Item:Q2571|<math>\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}</syntaxhighlight> || <math>\realpart@@{n} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(n, n))/(GAMMA(n)) < (1)/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Gamma[n, n],Gamma[n]] < Divide[1,2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
+| [https://dlmf.nist.gov/8.10.E13 8.10.E13] || <math qid="Q2571">\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}</syntaxhighlight> || <math>\realpart@@{n} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(n, n))/(GAMMA(n)) < (1)/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Gamma[n, n],Gamma[n]] < Divide[1,2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/8.10.E13 8.10.E13] || [[Item:Q2571|<math>\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}</syntaxhighlight> || <math>\realpart@@{n} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(2) < (GAMMA(n, n - 1))/(GAMMA(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2] < Divide[Gamma[n, n - 1],Gamma[n]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
+| [https://dlmf.nist.gov/8.10.E13 8.10.E13] || <math qid="Q2571">\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}</syntaxhighlight> || <math>\realpart@@{n} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(2) < (GAMMA(n, n - 1))/(GAMMA(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2] < Divide[Gamma[n, n - 1],Gamma[n]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
 |}
 </div>

8.10: Difference between revisions

Latest revision as of 11:18, 28 June 2021

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