18.21: 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/18.21#Ex3 18.21#Ex3] | | | [https://dlmf.nist.gov/18.21#Ex3 18.21#Ex3] || <math qid="Q5856">\CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{-(x), -(n)}, {}, -Divide[1,a]]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || - | ||
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| [https://dlmf.nist.gov/18.21.E9 18.21.E9] | | | [https://dlmf.nist.gov/18.21.E9 18.21.E9] || <math qid="Q5863">\lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[(2*a)^(Divide[1,2]*n)* HypergeometricPFQ[{-(n), -((2*a)^(Divide[1,2])* x + a)}, {}, -Divide[1,a]], a -> Infinity, GenerateConditions->None] == (- 1)^(n)* HermiteH[n, x]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || - | ||
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Latest revision as of 11:47, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.21#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a}}
\CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{-(x), -(n)}, {}, -Divide[1,a]]
|
Missing Macro Error | Missing Macro Error | - | - |
| 18.21.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x}}
\lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
Limit[(2*a)^(Divide[1,2]*n)* HypergeometricPFQ[{-(n), -((2*a)^(Divide[1,2])* x + a)}, {}, -Divide[1,a]], a -> Infinity, GenerateConditions->None] == (- 1)^(n)* HermiteH[n, x]
|
Missing Macro Error | Missing Macro Error | - | - |