Bessel function of the second kind: Representations through more general functions (formula 03.03.26.0043)

BesselY

$Mathematica Notation$

Bessel-Type Functions

BesselY[nu,z]

Representations through more general functions

Through Meijer G

Classical cases involving ₀F^~₁

http://functions.wolfram.com/03.03.26.0043.01

Input Form

BesselY[\[Nu], z] Hypergeometric0F1Regularized[b, -(z^2/4)] == (-(2^(-1 + b)/Sqrt[Pi])) MeijerG[{{(1 - b)/2, 1 - b/2}, {(1 - \[Nu])/2}}, {{-(\[Nu]/2), \[Nu]/2}, {(1 - \[Nu])/2, 1 - b - \[Nu]/2, 1 - b + \[Nu]/2}}, z^2] /; !(Element[-b - \[Nu], Integers] && -b - \[Nu] >= 0) && !(Element[-b + \[Nu], Integers] && -b + \[Nu] >= 0) && Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

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