Struve function H: Series representations (formula 03.09.06.0023)

StruveH

$Mathematica Notation$

Bessel-Type Functions

StruveH[nu,z]

Series representations

Generalized power series

Expansions on branch cuts

For the function itself

http://functions.wolfram.com/03.09.06.0023.01

Input Form

StruveH[\[Nu], z] == Sqrt[Pi] Gamma[2 + \[Nu]] (x/4)^(\[Nu] + 1) Exp[2 \[Nu] Pi I Floor[Arg[z - x]/(2 Pi)]] Sum[(2^k/(x^k k!)) HypergeometricPFQRegularized[{1, 1 + \[Nu]/2, (3 + \[Nu])/2}, {3/2, 1 + (\[Nu] - k)/2, (3 - k + \[Nu])/2, 3/2 + \[Nu]}, -(x^2/4)] (z - x)^k, {k, 0, Infinity}] /; Element[x, Reals] && x < 0

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)

2007-05-02