Hermite function: Series representations (formula 07.01.06.0006)

HermiteH

$Mathematica Notation$

Hypergeometric Functions

HermiteH[nu,z]

Series representations

Asymptotic series expansions

http://functions.wolfram.com/07.01.06.0006.01

Input Form

HermiteH[\[Nu], z] \[Proportional] (-((Sin[\[Nu] Pi] (z^2)^(-\[Nu]/2 - 1))/(2 Sqrt[Pi]))) (E^z^2 (Sqrt[z^2] - z) Gamma[\[Nu] + 1] HypergeometricPFQ[ {(1 + \[Nu])/2, (2 + \[Nu])/2}, {}, 1/z^2] + 2^\[Nu] Sqrt[Pi] Sqrt[-z^2] (-z^4)^(\[Nu]/2) (Sqrt[-z^2] Csc[(\[Nu] Pi)/2] + z Sec[(\[Nu] Pi)/2]) HypergeometricPFQ[{-(\[Nu]/2), (1 - \[Nu])/2}, {}, -(1/z^2)]) /; (Abs[z] -> Infinity)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HermiteH[n, z]