relation to generalized hypergeometric functions

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1: 16.7 Relations to Other Functions

§16.7 Relations to Other Functions

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2: 16.24 Physical Applications

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§16.24(iii) $\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ Symbols

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3: 16.18 Special Cases

§16.18 Special Cases

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4: 18.34 Bessel Polynomials

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§18.34(i) Definitions and Recurrence Relation

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18.34.1 $$y_n(x;a)={}_2{}^{}F_0^{}(\genfrac{}{}{0pt}{}{-n,n+a-1}{-};-\frac{x}{2})={\left(n+a-1\right)}_n{\left(\frac{x}{2}\right)}^n{}_1{}^{}F_1^{}(\genfrac{}{}{0pt}{}{-n}{-2n-a+2};\frac{2}{x}).$$

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Defines:

$y_n(x;a)$: Bessel polynomial

Symbols:

${}_p{}^{}F_q^{}(a_1,\mathrm{\dots },a_p;b_1,\mathrm{\dots },b_q;z)$ or ${}_p{}^{}F_q^{}(\genfrac{}{}{0pt}{}{a_1,\mathrm{\dots },a_p}{b_1,\mathrm{\dots },b_q};z)$: alternatively ${}_p{}^{}F_q^{}(𝐚;𝐛;z)$ or ${}_p{}^{}F_q^{}(\genfrac{}{}{0pt}{}{𝐚}{𝐛};z)$
generalized hypergeometric function, ${}_1{}^{}F_1^{}(a;b;z)$: $=M(a,b,z)$ notation for the Kummer confluent hypergeometric function, ${\left(a\right)}_n$: Pochhammer’s symbol (or shifted factorial), $n$: nonnegative integer and $x$: real variable

Referenced by:

§18.34(i)

Permalink:

http://dlmf.nist.gov/18.34.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §18.34(i), §18.34 and Ch.18

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5: 7.11 Relations to Other Functions

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Generalized Hypergeometric Functions

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6: 10.39 Relations to Other Functions

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Generalized Hypergeometric Functions and Hypergeometric Function

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7: 10.16 Relations to Other Functions

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Generalized Hypergeometric Functions

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8: 16.17 Definition

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9: 18.20 Hahn Class: Explicit Representations

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§18.20(ii) Hypergeometric Function and Generalized Hypergeometric Functions

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10: 18.30 Associated OP’s

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Associated Jacobi Polynomials

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