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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=7/2 > For fixed z and a1=1/2, a2=1/2, a3=7/2, b1=1





http://functions.wolfram.com/07.27.03.amr3.01









  


  










Input Form





HypergeometricPFQ[{1/2, 1/2, 7/2}, {1, 3}, z] == (128 (2 + 7 z) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/(135 Pi^2 z^2) + (128 (-2 - 7 z) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/(135 Pi^2 z^2) + (64 Sqrt[1 - z] (4 + 11 z - 24 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/(135 Pi^2 (-1 + z) z^2) + (32 (4 + 13 z) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(135 Pi^2 z^2) + (32 Sqrt[1 - z] (-4 - 11 z + 24 z^2) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/ (135 Pi^2 (-1 + z) z^2)










Standard Form





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MathML Form







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type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -24 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <ci> z </ci> </apply> <cn type='integer'> 4 </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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn 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<power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </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