Modified Bessel function of the first kind: Representations through more general functions (formula 03.02.26.0104)

BesselI

$Mathematica Notation$

Bessel-Type Functions

BesselI[nu,z]

Representations through more general functions

Through Meijer G

Classical cases involving ₀F₁

http://functions.wolfram.com/03.02.26.0104.01

Input Form

BesselI[\[Nu], 2 Sqrt[z]] Hypergeometric0F1[-1 - \[Nu], z] == ((2^(-(3/2) - \[Nu]) Gamma[-1 - \[Nu]])/Pi) ((-Pi^(3/2)) MeijerG[{{(2 + \[Nu])/2, (3 + \[Nu])/2}, {(1/4) (5 + 2 \[Nu])}}, {{(4 + \[Nu])/2}, {-(\[Nu]/2), \[Nu]/2, 2 + (3 \[Nu])/2, (1/4) (5 + 2 \[Nu])}}, 4 z] + 2^(3/2 + \[Nu]) z^(\[Nu]/2) (1 + \[Nu]) Sin[Pi \[Nu]])

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