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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case 0F3





http://functions.wolfram.com/07.31.03.0158.01









  


  








Input Form





HypergeometricPFQ[{}, {1/2, b, -b}, -z] == ((Pi Csc[2 b Pi])/(Sqrt[2] b)) ((b z^(1/4) BesselI[2 b, 2 Sqrt[2] z^(1/4)] + Sqrt[2] Sqrt[z] BesselI[1 + 2 b, 2 Sqrt[2] z^(1/4)]) BesselJ[1 - 2 b, 2 Sqrt[2] z^(1/4)] + b (Sqrt[2] b BesselI[2 b, 2 Sqrt[2] z^(1/4)] + z^(1/4) BesselI[1 + 2 b, 2 Sqrt[2] z^(1/4)]) BesselJ[-2 b, 2 Sqrt[2] z^(1/4)] + b ((-z^(1/4)) BesselI[1 - 2 b, 2 Sqrt[2] z^(1/4)] + Sqrt[2] b BesselI[-2 b, 2 Sqrt[2] z^(1/4)]) BesselJ[2 b, 2 Sqrt[2] z^(1/4)] + (Sqrt[2] Sqrt[z] BesselI[1 - 2 b, 2 Sqrt[2] z^(1/4)] - b z^(1/4) BesselI[-2 b, 2 Sqrt[2] z^(1/4)]) BesselJ[1 + 2 b, 2 Sqrt[2] z^(1/4)])








Standard Form





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MathML Form







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<times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </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