Formula:KLS:09.08:95

<< Formula:KLS:09.08:94

formula in Jacobi: Special cases

Formula:KLS:09.08:96 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \expe^{xt}\,\HyperpFq{0}{1}@@{-}{1}{\frac{(x^2-1)t^2}{4}}= \sum_{n=0}^{\infty}\frac{\LegendrePoly{n}@{x}}{n!}t^n }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {{}_{p}F_{q}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P_{n}}}  : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:94

formula in Jacobi: Special cases

Formula:KLS:09.08:96 >>