Elementary Functions - 5.2 Definitions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 5.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{z} = \int_{0}^{\infty}e^{-t}t^{z-1}\diff{t}}
\EulerGamma@{z} = \int_{0}^{\infty}e^{-t}t^{z-1}\diff{t} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z} > 0} | GAMMA(z) = int(exp(- t)*(t)^(z - 1), t = 0..infinity)
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Gamma[z] == Integrate[Exp[- t]*(t)^(z - 1), {t, 0, Infinity}, GenerateConditions->None]
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Successful | Successful | - | Successful [Tested: 5] |
| 5.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{z} = \EulerGamma'@{z}/\EulerGamma@{z}}
\digamma@{z} = \EulerGamma'@{z}/\EulerGamma@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z} > 0} | Psi(z) = diff( GAMMA(z), z$(1) )/GAMMA(z)
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PolyGamma[z] == D[Gamma[z], {z, 1}]/Gamma[z]
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Successful | Successful | - | Successful [Tested: 1] |
| 5.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{0} = 1}
\Pochhammersym{a}{0} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | pochhammer(a, 0) = 1
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Pochhammer[a, 0] == 1
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Successful | Successful | - | Successful [Tested: 6] |
| 5.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{n} = \EulerGamma@{a+n}/\EulerGamma@{a}}
\Pochhammersym{a}{n} = \EulerGamma@{a+n}/\EulerGamma@{a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(a+n)} > 0, \realpart@@{a} > 0} | pochhammer(a, n) = GAMMA(a + n)/GAMMA(a)
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Pochhammer[a, n] == Gamma[a + n]/Gamma[a]
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Successful | Successful | - | Successful [Tested: 3] |
| 5.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{-a}{n} = (-1)^{n}\Pochhammersym{a-n+1}{n}}
\Pochhammersym{-a}{n} = (-1)^{n}\Pochhammersym{a-n+1}{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | pochhammer(- a, n) = (- 1)^(n)* pochhammer(a - n + 1, n)
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Pochhammer[- a, n] == (- 1)^(n)* Pochhammer[a - n + 1, n]
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Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 5.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{2n} = 2^{2n}\Pochhammersym{\frac{a}{2}}{n}\Pochhammersym{\frac{a+1}{2}}{n}}
\Pochhammersym{a}{2n} = 2^{2n}\Pochhammersym{\frac{a}{2}}{n}\Pochhammersym{\frac{a+1}{2}}{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | pochhammer(a, 2*n) = (2)^(2*n)* pochhammer((a)/(2), n)*pochhammer((a + 1)/(2), n)
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Pochhammer[a, 2*n] == (2)^(2*n)* Pochhammer[Divide[a,2], n]*Pochhammer[Divide[a + 1,2], n]
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Successful | Successful | - | Successful [Tested: 18] |
| 5.2#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{a}{2n+1} = 2^{2n+1}\Pochhammersym{\frac{a}{2}}{n+1}\Pochhammersym{\frac{a+1}{2}}{n}}
\Pochhammersym{a}{2n+1} = 2^{2n+1}\Pochhammersym{\frac{a}{2}}{n+1}\Pochhammersym{\frac{a+1}{2}}{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | pochhammer(a, 2*n + 1) = (2)^(2*n + 1)* pochhammer((a)/(2), n + 1)*pochhammer((a + 1)/(2), n)
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Pochhammer[a, 2*n + 1] == (2)^(2*n + 1)* Pochhammer[Divide[a,2], n + 1]*Pochhammer[Divide[a + 1,2], n]
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Successful | Successful | - | Successful [Tested: 18] |