18.21: Difference between revisions

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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] || [[Item:Q5856|<math>\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 || - || -
| [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] || [[Item:Q5863|<math>\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 || - || -
| [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 C n ⁡ ( x ; a ) = C x ⁡ ( n ; a ) Charlier-polynomial-C 𝑛 𝑥 𝑎 Charlier-polynomial-C 𝑥 𝑛 𝑎 {\displaystyle{\displaystyle C_{n}\left(x;a\right)=C_{x}\left(n;a\right)}}
\CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a}		 

Error

HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{-(x), -(n)}, {}, -Divide[1,a]]
Missing Macro Error Missing Macro Error - -
18.21.E9 lim a → ∞ ⁡ ( 2 ⁢ a ) 1 2 ⁢ n ⁢ C n ⁡ ( ( 2 ⁢ a ) 1 2 ⁢ x + a ; a ) = ( - 1 ) n ⁢ H n ⁡ ( x ) subscript → 𝑎 superscript 2 𝑎 1 2 𝑛 Charlier-polynomial-C 𝑛 superscript 2 𝑎 1 2 𝑥 𝑎 𝑎 superscript 1 𝑛 Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{a\to\infty}(2a)^{\frac{1}{2}n}C_{n}\left((2a% )^{\frac{1}{2}}x+a;a\right)=(-1)^{n}H_{n}\left(x\right)}}
\lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x}		 

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 - -
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