Modified Bessel function of the second kind: Integration (formula 03.04.21.0021)

BesselK

$Mathematica Notation$

Bessel-Type Functions

BesselK[nu,z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving exponential function and a power function

Involving exp and power

Linear arguments

http://functions.wolfram.com/03.04.21.0021.01

Input Form

Integrate[(z^(\[Alpha] - 1) BesselK[\[Nu], a z])/E^(a z), z] == (2^(-1 - \[Nu]) Sqrt[Pi] z^\[Alpha] Csc[Pi \[Nu]] (Gamma[1/2 - \[Nu]] Gamma[\[Alpha] - \[Nu]] HypergeometricPFQRegularized[ {1/2 - \[Nu], \[Alpha] - \[Nu]}, {1 - 2 \[Nu], 1 + \[Alpha] - \[Nu]}, -2 a z] - 4^\[Nu] (a z)^(2 \[Nu]) Gamma[1/2 + \[Nu]] Gamma[\[Alpha] + \[Nu]] HypergeometricPFQRegularized[ {1/2 + \[Nu], \[Alpha] + \[Nu]}, {1 + \[Alpha] + \[Nu], 1 + 2 \[Nu]}, -2 a z]))/(a z)^\[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)

2001-10-29