Modified Bessel function of the second kind: Representations through more general functions (formula 03.04.26.0086)

BesselK

$Mathematica Notation$

Bessel-Type Functions

BesselK[nu,z]

Representations through more general functions

Through Meijer G

Classical cases involving ₀F₁

http://functions.wolfram.com/03.04.26.0086.01

Input Form

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

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