Bessel function of the second kind: Representations through more general functions (formula 03.03.26.0127)

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/03.03.26.0127.01

Input Form

BesselY[\[Nu], z] Hypergeometric0F1Regularized[-n - \[Nu], -(z^2/4)] == (2^(-1 - n - \[Nu])/Sqrt[Pi]) ((-1)^n MeijerG[{{(1/2) (1 + n + \[Nu]), (1/2) (2 + n + \[Nu])}, {(1 - \[Nu])/2}}, {{1 + n + \[Nu]/2, -(\[Nu]/2)}, {1 + n + (3 \[Nu])/2, \[Nu]/2, (1 - \[Nu])/2}}, z^2] + 2 z^\[Nu] Cot[\[Nu] Pi] Sum[(((-1)^(k + Floor[(1 + n)/2]) z^(2 k) Gamma[1/2 + k - n + Floor[n/2]])/(k! Gamma[k - n - \[Nu]] Gamma[1 + k + \[Nu]])) Pochhammer[1 - k + Floor[n/2], n - Floor[n/2]], {k, 0, Floor[n/2]}]) /; Element[n, Integers] && n >= 0 && Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

Standard Form

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MathML Form

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</apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <lt /> <apply> <arg /> <ci> z </ci> </apply> <leq /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02