10.14: Difference between revisions
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Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ||
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| [https://dlmf.nist.gov/10.14#Ex1 10.14#Ex1] | | | [https://dlmf.nist.gov/10.14#Ex1 10.14#Ex1] || <math qid="Q3137">|\BesselJ{\nu}@{x}| \leq 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{\nu}@{x}| \leq 1</syntaxhighlight> || <math>\nu \geq 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(nu, x)) <= 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[\[Nu], x]] <= 1</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/10.14#Ex2 10.14#Ex2] | | | [https://dlmf.nist.gov/10.14#Ex2 10.14#Ex2] || <math qid="Q3138">|\BesselJ{\nu}@{x}| \leq 2^{-\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{\nu}@{x}| \leq 2^{-\frac{1}{2}}</syntaxhighlight> || <math>\nu \geq 1, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(nu, x)) <= (2)^(-(1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[\[Nu], x]] <= (2)^(-Divide[1,2])</syntaxhighlight> || Failure || Failure || Successful [Tested: 2] || Successful [Tested: 2] | ||
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| [https://dlmf.nist.gov/10.14.E2 10.14.E2] | | | [https://dlmf.nist.gov/10.14.E2 10.14.E2] || <math qid="Q3139">0 < \BesselJ{\nu}@{\nu}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>0 < \BesselJ{\nu}@{\nu}</syntaxhighlight> || <math>\nu > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>0 < BesselJ(nu, nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>0 < BesselJ[\[Nu], \[Nu]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/10.14.E2 10.14.E2] | | | [https://dlmf.nist.gov/10.14.E2 10.14.E2] || <math qid="Q3139">\BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}}</syntaxhighlight> || <math>\nu > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselJ(nu, nu) < ((2)^((1)/(3)))/((3)^((2)/(3))* GAMMA((2)/(3))*(nu)^((1)/(3)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[\[Nu], \[Nu]] < Divide[(2)^(Divide[1,3]),(3)^(Divide[2,3])* Gamma[Divide[2,3]]*\[Nu]^(Divide[1,3])]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/10.14.E3 10.14.E3] | | | [https://dlmf.nist.gov/10.14.E3 10.14.E3] || <math qid="Q3140">|\BesselJ{n}@{z}| \leq e^{|\imagpart@@{z}|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{n}@{z}| \leq e^{|\imagpart@@{z}|}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(n, z)) <= exp(abs(Im(z)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[n, z]] <= Exp[Abs[Im[z]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/10.14.E4 10.14.E4] | | | [https://dlmf.nist.gov/10.14.E4 10.14.E4] || <math qid="Q3141">|\BesselJ{\nu}@{z}| \leq \frac{|\tfrac{1}{2}z|^{\nu}e^{|\imagpart@@{z}|}}{\EulerGamma@{\nu+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{\nu}@{z}| \leq \frac{|\tfrac{1}{2}z|^{\nu}e^{|\imagpart@@{z}|}}{\EulerGamma@{\nu+1}}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(\nu+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(nu, z)) <= ((abs((1)/(2)*z))^(nu)* exp(abs(Im(z))))/(GAMMA(nu + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[\[Nu], z]] <= Divide[(Abs[Divide[1,2]*z])^\[Nu]* Exp[Abs[Im[z]]],Gamma[\[Nu]+ 1]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/10.14.E5 10.14.E5] | | | [https://dlmf.nist.gov/10.14.E5 10.14.E5] || <math qid="Q3142">|\BesselJ{\nu}@{\nu x}| \leq \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{\nu}@{\nu x}| \leq \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}</syntaxhighlight> || <math>\nu \geq 0, 0 < x, x \leq 1, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(nu, nu*x)) <= ((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[\[Nu], \[Nu]*x]] <= Divide[(x)^\[Nu]* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^\[Nu]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Skip - No test values generated | ||
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| [https://dlmf.nist.gov/10.14.E7 10.14.E7] | | | [https://dlmf.nist.gov/10.14.E7 10.14.E7] || <math qid="Q3144">1 \leq \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>1 \leq \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}}</syntaxhighlight> || <math>\nu \geq 0, 0 < x, x \leq 1, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>1 <= (BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu))</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 <= Divide[BesselJ[\[Nu], \[Nu]*x],(x)^\[Nu]* BesselJ[\[Nu], \[Nu]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Skip - No test values generated | ||
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| [https://dlmf.nist.gov/10.14.E7 10.14.E7] | | | [https://dlmf.nist.gov/10.14.E7 10.14.E7] || <math qid="Q3144">\frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} \leq e^{\nu(1-x)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} \leq e^{\nu(1-x)}</syntaxhighlight> || <math>\nu \geq 0, 0 < x, x \leq 1, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu)) <= exp(nu*(1 - x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[BesselJ[\[Nu], \[Nu]*x],(x)^\[Nu]* BesselJ[\[Nu], \[Nu]]] <= Exp[\[Nu]*(1 - x)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Skip - No test values generated | ||
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| [https://dlmf.nist.gov/10.14.E8 10.14.E8] | | | [https://dlmf.nist.gov/10.14.E8 10.14.E8] || <math qid="Q3145">|\BesselJ{n}@{nz}| \leq \frac{\left|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}\right|^{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{n}@{nz}| \leq \frac{\left|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}\right|^{n}}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(n, n*z)) <= (abs((z)^(n)* exp(n*(1 - (z)^(2))^((1)/(2)))))/((abs(1 +(1 - (z)^(2))^((1)/(2))))^(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[n, n*z]] <= Divide[Abs[(z)^(n)* Exp[n*(1 - (z)^(2))^(Divide[1,2])]],(Abs[1 +(1 - (z)^(2))^(Divide[1,2])])^(n)]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/10.14.E9 10.14.E9] | | | [https://dlmf.nist.gov/10.14.E9 10.14.E9] || <math qid="Q3146">|\BesselJ{n}@{nz}| \leq 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\BesselJ{n}@{nz}| \leq 1</syntaxhighlight> || <math>n = 0, \realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>abs(BesselJ(n, n*z)) <= 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[BesselJ[n, n*z]] <= 1</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 21] | ||
|} | |} | ||
</div> | </div> |
Latest revision as of 11:23, 28 June 2021
DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|---|
10.14#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{x}| \leq 1}
|\BesselJ{\nu}@{x}| \leq 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \geq 0, \realpart@@{(\nu+k+1)} > 0} | abs(BesselJ(nu, x)) <= 1
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Abs[BesselJ[\[Nu], x]] <= 1
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
10.14#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{x}| \leq 2^{-\frac{1}{2}}}
|\BesselJ{\nu}@{x}| \leq 2^{-\frac{1}{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \geq 1, \realpart@@{(\nu+k+1)} > 0} | abs(BesselJ(nu, x)) <= (2)^(-(1)/(2))
|
Abs[BesselJ[\[Nu], x]] <= (2)^(-Divide[1,2])
|
Failure | Failure | Successful [Tested: 2] | Successful [Tested: 2] |
10.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \BesselJ{\nu}@{\nu}}
0 < \BesselJ{\nu}@{\nu} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu > 0, \realpart@@{(\nu+k+1)} > 0} | 0 < BesselJ(nu, nu)
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0 < BesselJ[\[Nu], \[Nu]]
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
10.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}}}
\BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu > 0, \realpart@@{(\nu+k+1)} > 0} | BesselJ(nu, nu) < ((2)^((1)/(3)))/((3)^((2)/(3))* GAMMA((2)/(3))*(nu)^((1)/(3)))
|
BesselJ[\[Nu], \[Nu]] < Divide[(2)^(Divide[1,3]),(3)^(Divide[2,3])* Gamma[Divide[2,3]]*\[Nu]^(Divide[1,3])]
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
10.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{z}| \leq e^{|\imagpart@@{z}|}}
|\BesselJ{n}@{z}| \leq e^{|\imagpart@@{z}|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(n+k+1)} > 0} | abs(BesselJ(n, z)) <= exp(abs(Im(z)))
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Abs[BesselJ[n, z]] <= Exp[Abs[Im[z]]]
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Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
10.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{z}| \leq \frac{|\tfrac{1}{2}z|^{\nu}e^{|\imagpart@@{z}|}}{\EulerGamma@{\nu+1}}}
|\BesselJ{\nu}@{z}| \leq \frac{|\tfrac{1}{2}z|^{\nu}e^{|\imagpart@@{z}|}}{\EulerGamma@{\nu+1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\nu+k+1)} > 0, \realpart@@{(\nu+1)} > 0} | abs(BesselJ(nu, z)) <= ((abs((1)/(2)*z))^(nu)* exp(abs(Im(z))))/(GAMMA(nu + 1))
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Abs[BesselJ[\[Nu], z]] <= Divide[(Abs[Divide[1,2]*z])^\[Nu]* Exp[Abs[Im[z]]],Gamma[\[Nu]+ 1]]
|
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
10.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{\nu x}| \leq \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}}
|\BesselJ{\nu}@{\nu x}| \leq \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \geq 0, 0 < x, x \leq 1, \realpart@@{(\nu+k+1)} > 0} | abs(BesselJ(nu, nu*x)) <= ((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu))
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Abs[BesselJ[\[Nu], \[Nu]*x]] <= Divide[(x)^\[Nu]* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^\[Nu]]
|
Failure | Failure | Successful [Tested: 3] | Skip - No test values generated |
10.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}}}
1 \leq \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \geq 0, 0 < x, x \leq 1, \realpart@@{(\nu+k+1)} > 0} | 1 <= (BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu))
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1 <= Divide[BesselJ[\[Nu], \[Nu]*x],(x)^\[Nu]* BesselJ[\[Nu], \[Nu]]]
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Failure | Failure | Successful [Tested: 3] | Skip - No test values generated |
10.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} \leq e^{\nu(1-x)}}
\frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} \leq e^{\nu(1-x)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu \geq 0, 0 < x, x \leq 1, \realpart@@{(\nu+k+1)} > 0} | (BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu)) <= exp(nu*(1 - x))
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Divide[BesselJ[\[Nu], \[Nu]*x],(x)^\[Nu]* BesselJ[\[Nu], \[Nu]]] <= Exp[\[Nu]*(1 - x)]
|
Failure | Failure | Successful [Tested: 3] | Skip - No test values generated |
10.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{nz}| \leq \frac{\left|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}\right|^{n}}}
|\BesselJ{n}@{nz}| \leq \frac{\left|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}\right|^{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(n+k+1)} > 0} | abs(BesselJ(n, n*z)) <= (abs((z)^(n)* exp(n*(1 - (z)^(2))^((1)/(2)))))/((abs(1 +(1 - (z)^(2))^((1)/(2))))^(n))
|
Abs[BesselJ[n, n*z]] <= Divide[Abs[(z)^(n)* Exp[n*(1 - (z)^(2))^(Divide[1,2])]],(Abs[1 +(1 - (z)^(2))^(Divide[1,2])])^(n)]
|
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
10.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{nz}| \leq 1}
|\BesselJ{n}@{nz}| \leq 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n = 0, \realpart@@{(n+k+1)} > 0} | abs(BesselJ(n, n*z)) <= 1
|
Abs[BesselJ[n, n*z]] <= 1
|
Failure | Failure | Error | Successful [Tested: 21] |