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SphericalBesselJ




Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Differentiation > Low-order differentiation > With respect to nu





http://functions.wolfram.com/03.21.20.0003.01









  


  








Input Form





Derivative[1, 0][SphericalBesselJ][n, z] == (-((2 (2 z)^(-n - 1))/n!)) Sum[(-1)^k 2^(2 k) Binomial[n, 2 k] (2 n - 2 k)! ((PolyGamma[k + 1/2] - PolyGamma[k - n + 1/2]) Sin[z] - Sin[z] CosIntegral[2 z] + Cos[z] SinIntegral[2 z]) z^(2 k), {k, 0, Floor[n/2]}] + (2/((2 z)^n n!)) Sum[(-1)^k 2^(2 k) Binomial[n, 2 k + 1] (2 n - 2 k - 1)! ((PolyGamma[k + 3/2] - PolyGamma[k - n + 1/2]) Cos[z] - Sin[z] SinIntegral[2 z] - Cos[z] CosIntegral[2 z]) z^(2 k), {k, 0, Floor[(n - 1)/2]}] /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <sin /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <cos /> <ci> z </ci> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Contributed by





Brychkov Yu.A. (2005)


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





2007-05-02