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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=-7/2, a2>=-7/2 > For fixed z and a1=-7/2, a2=-1/2, a3>=-1/2 > For fixed z and a1=-7/2, a2=-1/2, a3=1/2 > For fixed z and a1=-7/2, a2=-1/2, a3=1/2, b1=3





http://functions.wolfram.com/07.27.03.4840.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), -(1/2), 1/2}, {3, 3}, z] == (1/(108056025 Pi^2 z^2)) (512 (-205919 - 3138898 z + 3319590 z^2 + 84932 z^3 - 6728 z^4 + 384 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(108056025 Pi^2 z^2)) (512 Sqrt[1 - z] (157409 + 2165604 z - 1030464 z^2 - 1613 z^3 + 96 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(108056025 Pi^2 z^2)) (512 (-205919 - 3138898 z + 3319590 z^2 + 84932 z^3 - 6728 z^4 + 384 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(108056025 Pi^2 z^2)) (256 Sqrt[1 - z] (-157409 - 2165604 z + 1030464 z^2 + 1613 z^3 - 96 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(108056025 Pi^2 z^2)) (256 (-157409 - 2099027 z + 3561342 z^2 + 42671 z^3 - 3376 z^4 + 192 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)










Standard Form





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MathML Form







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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 84932 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3319590 </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'> 3138898 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -205919 </cn> </apply> <apply> <power /> <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 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 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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'> 108056025 </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