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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=1/2, a2>=1/2 > For fixed z and a1=1/2, a2=1/2, a3>=1/2 > For fixed z and a1=1/2, a2=1/2, a3=1/2 > For fixed z and a1=1/2, a2=1/2, a3=1/2, b1=1





http://functions.wolfram.com/07.27.03.amal.01









  


  








Input Form





HypergeometricPFQ[{1/2, 1/2, 1/2}, {1, 4}, z] == -((256 (32 - 121 z + 197 z^2) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/ (1125 Pi^2 z^3)) + (256 (32 - 121 z + 197 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (1125 Pi^2 z^3) + (128 Sqrt[1 - z] (64 - 226 z + 345 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (1125 Pi^2 z^3) - (64 Sqrt[1 - z] (64 - 226 z + 345 z^2) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(1125 Pi^2 z^3) + (64 (-64 + 258 z - 452 z^2 + 225 z^3) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/ (1125 Pi^2 z^3)








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1125 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 197 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 121 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 32 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> 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/> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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