5.2: 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/5.2.E1 5.2.E1] | | | [https://dlmf.nist.gov/5.2.E1 5.2.E1] || <math qid="Q2026">\EulerGamma@{z} = \int_{0}^{\infty}e^{-t}t^{z-1}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerGamma@{z} = \int_{0}^{\infty}e^{-t}t^{z-1}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(z) = int(exp(- t)*(t)^(z - 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[z] == Integrate[Exp[- t]*(t)^(z - 1), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 5] | ||
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| [https://dlmf.nist.gov/5.2.E2 5.2.E2] | | | [https://dlmf.nist.gov/5.2.E2 5.2.E2] || <math qid="Q2027">\digamma@{z} = \EulerGamma'@{z}/\EulerGamma@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\digamma@{z} = \EulerGamma'@{z}/\EulerGamma@{z}</syntaxhighlight> || <math>\realpart@@{z} > 0</math> || <syntaxhighlight lang=mathematica>Psi(z) = diff( GAMMA(z), z$(1) )/GAMMA(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>PolyGamma[z] == D[Gamma[z], {z, 1}]/Gamma[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1] | ||
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| [https://dlmf.nist.gov/5.2#Ex1 5.2#Ex1] | | | [https://dlmf.nist.gov/5.2#Ex1 5.2#Ex1] || <math qid="Q2029">\Pochhammersym{a}{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Pochhammersym{a}{0} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>pochhammer(a, 0) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pochhammer[a, 0] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 6] | ||
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| [https://dlmf.nist.gov/5.2.E5 5.2.E5] | | | [https://dlmf.nist.gov/5.2.E5 5.2.E5] || <math qid="Q2031">\Pochhammersym{a}{n} = \EulerGamma@{a+n}/\EulerGamma@{a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Pochhammersym{a}{n} = \EulerGamma@{a+n}/\EulerGamma@{a}</syntaxhighlight> || <math>\realpart@@{(a+n)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>pochhammer(a, n) = GAMMA(a + n)/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pochhammer[a, n] == Gamma[a + n]/Gamma[a]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3] | ||
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| [https://dlmf.nist.gov/5.2.E6 5.2.E6] | | | [https://dlmf.nist.gov/5.2.E6 5.2.E6] || <math qid="Q2032">\Pochhammersym{-a}{n} = (-1)^{n}\Pochhammersym{a-n+1}{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Pochhammersym{-a}{n} = (-1)^{n}\Pochhammersym{a-n+1}{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>pochhammer(- a, n) = (- 1)^(n)* pochhammer(a - n + 1, n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pochhammer[- a, n] == (- 1)^(n)* Pochhammer[a - n + 1, n]</syntaxhighlight> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18] | ||
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| [https://dlmf.nist.gov/5.2#Ex3 5.2#Ex3] | | | [https://dlmf.nist.gov/5.2#Ex3 5.2#Ex3] || <math qid="Q2034">\Pochhammersym{a}{2n} = 2^{2n}\Pochhammersym{\frac{a}{2}}{n}\Pochhammersym{\frac{a+1}{2}}{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Pochhammersym{a}{2n} = 2^{2n}\Pochhammersym{\frac{a}{2}}{n}\Pochhammersym{\frac{a+1}{2}}{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>pochhammer(a, 2*n) = (2)^(2*n)* pochhammer((a)/(2), n)*pochhammer((a + 1)/(2), n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pochhammer[a, 2*n] == (2)^(2*n)* Pochhammer[Divide[a,2], n]*Pochhammer[Divide[a + 1,2], n]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 18] | ||
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| [https://dlmf.nist.gov/5.2#Ex4 5.2#Ex4] | | | [https://dlmf.nist.gov/5.2#Ex4 5.2#Ex4] || <math qid="Q2035">\Pochhammersym{a}{2n+1} = 2^{2n+1}\Pochhammersym{\frac{a}{2}}{n+1}\Pochhammersym{\frac{a+1}{2}}{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Pochhammersym{a}{2n+1} = 2^{2n+1}\Pochhammersym{\frac{a}{2}}{n+1}\Pochhammersym{\frac{a+1}{2}}{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>pochhammer(a, 2*n + 1) = (2)^(2*n + 1)* pochhammer((a)/(2), n + 1)*pochhammer((a + 1)/(2), n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pochhammer[a, 2*n + 1] == (2)^(2*n + 1)* Pochhammer[Divide[a,2], n + 1]*Pochhammer[Divide[a + 1,2], n]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 18] | ||
|} | |} | ||
</div> | </div> | ||
Latest revision as of 11:12, 28 June 2021
| 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)
|
Gamma[z] == Integrate[Exp[- t]*(t)^(z - 1), {t, 0, Infinity}, GenerateConditions->None]
|
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]
|
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
|
Pochhammer[a, 0] == 1
|
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)
|
Pochhammer[a, n] == Gamma[a + n]/Gamma[a]
|
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)
|
Pochhammer[- a, n] == (- 1)^(n)* Pochhammer[a - n + 1, n]
|
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)
|
Pochhammer[a, 2*n] == (2)^(2*n)* Pochhammer[Divide[a,2], n]*Pochhammer[Divide[a + 1,2], n]
|
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)
|
Pochhammer[a, 2*n + 1] == (2)^(2*n + 1)* Pochhammer[Divide[a,2], n + 1]*Pochhammer[Divide[a + 1,2], n]
|
Successful | Successful | - | Successful [Tested: 18] |