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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=-5/2, a2>=-5/2 > For fixed z and a1=-5/2, a2=7/2, a3>=7/2 > For fixed z and a1=-5/2, a2=7/2, a3=7/2 > For fixed z and a1=-5/2, a2=7/2, a3=7/2, b1=-1/2





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









  


  










Input Form





HypergeometricPFQ[{-(5/2), 7/2, 7/2}, {-(1/2), 1}, -z] == (1/(15 Pi (1 + z)^4)) (4 (27 - 1590 z - 20793 z^2 - 69632 z^3 - 99584 z^4 - 65536 z^5 - 16384 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(15 Pi (1 + z)^(7/2))) (4 (27 - 1590 z - 20793 z^2 - 69632 z^3 - 99584 z^4 - 65536 z^5 - 16384 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(15 Pi z (1 + z)^(7/2))) (4 (15 - 882 z - 16161 z^2 - 60624 z^3 - 92416 z^4 - 63488 z^5 - 16384 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(15 Pi z (1 + z)^3)) (4 (-15 + 843 z + 18498 z^2 + 83712 z^3 + 147968 z^4 + 114688 z^5 + 32768 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])










Standard Form





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MathML Form







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type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 15 </cn> <pi /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 63488 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 92416 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60624 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16161 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 882 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 15 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 15 </cn> <pi /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 32768 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 114688 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02