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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=5/2 > For fixed z and a1=-1/2, a2=-1/2, a3=5/2, b1=3





http://functions.wolfram.com/07.27.03.aiy5.01









  


  








Input Form





HypergeometricPFQ[{-(1/2), -(1/2), 5/2}, {3, 3}, z] == (512 (-77 + 246 z + 398 z^2) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/ (10125 Pi^2 z^2) - (512 Sqrt[1 - z] (-47 + 148 z + 120 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (10125 Pi^2 z^2) - (512 (-77 + 246 z + 398 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (10125 Pi^2 z^2) + (256 Sqrt[1 - z] (-47 + 148 z + 120 z^2) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(10125 Pi^2 z^2) + (256 (-47 + 164 z + 229 z^2) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/ (10125 Pi^2 z^2)








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 164 </cn> <ci> z </ci> </apply> <cn type='integer'> -47 </cn> </apply> <apply> <power /> <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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 10125 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </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