Orthogonal Polynomials - 18.21 Hahn Class: Interrelations
| 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]]
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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
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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]
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Missing Macro Error | Missing Macro Error | - | - |