Bessel function of the second kind: Differentiation (formula 03.03.20.0015)

BesselY

$Mathematica Notation$

Bessel-Type Functions

BesselY[nu,z]

Differentiation

Fractional integro-differentiation

With respect to z

http://functions.wolfram.com/03.03.20.0015.01

Input Form

D[BesselY[\[Nu], z], {z, \[Alpha]}] == 2^(\[Alpha] - 2 \[Nu]) Sqrt[Pi] z^(-\[Alpha] - \[Nu]) Csc[Pi \[Nu]] ((-16^\[Nu]) Gamma[1 - \[Nu]] HypergeometricPFQRegularized[ {(1 - \[Nu])/2, 1 - \[Nu]/2}, {1 - \[Nu], (1/2) (1 - \[Alpha] - \[Nu]), (1/2) (2 - \[Alpha] - \[Nu])}, -(z^2/4)] + z^(2 \[Nu]) Cos[Pi \[Nu]] Gamma[1 + \[Nu]] HypergeometricPFQRegularized[ {(1 + \[Nu])/2, (2 + \[Nu])/2}, {(1/2) (1 - \[Alpha] + \[Nu]), (1/2) (2 - \[Alpha] + \[Nu]), 1 + \[Nu]}, -(z^2/4)]) /; !Element[\[Nu], Integers]

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