Cosine: Integral transforms (formula 01.07.22.0007)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integral transforms

Hankel transforms

http://functions.wolfram.com/01.07.22.0007.01

Input Form

HankelTransform[t^(\[Alpha] - 1) Cos[t], {t, \[Nu]}, z] == (1/Gamma[1 + \[Nu]]) ((z^(1/2 + \[Nu]) Cos[(1/4) Pi (1 + 2 \[Alpha] + 2 \[Nu])] Gamma[1/2 + \[Alpha] + \[Nu]] Hypergeometric2F1[(1/4) (1 + 2 \[Alpha] + 2 \[Nu]), (1/4) (3 + 2 \[Alpha] + 2 \[Nu]), 1 + \[Nu], z^2])/2^\[Nu]) /; Re[\[Alpha] + \[Nu]] > -(1/2) && Re[\[Alpha]] < 1

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