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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=-3/2, a3>=-3/2 > For fixed z and a1=-5/2, a2=-3/2, a3=7/2 > For fixed z and a1=-5/2, a2=-3/2, a3=7/2, b1=3





http://functions.wolfram.com/07.27.03.a9e0.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), -(3/2), 7/2}, {3, 4}, z] == (1/(38201625 Pi^2 z^3)) (2048 (140 - 5983 z + 66971 z^2 + 693481 z^3 + 361492 z^4 + 4480 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(38201625 Pi^2 z^3)) (1024 Sqrt[1 - z] (280 - 8431 z + 91803 z^2 + 583409 z^3 + 219520 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(38201625 Pi^2 z^3)) (2048 (140 - 5983 z + 66971 z^2 + 693481 z^3 + 361492 z^4 + 4480 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(38201625 Pi^2 z^3)) (512 Sqrt[1 - z] (280 - 8431 z + 91803 z^2 + 583409 z^3 + 219520 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(38201625 Pi^2 z^3)) (512 (280 - 8571 z + 95126 z^2 + 846614 z^3 + 416652 z^4 + 4480 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)










Standard Form





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MathML Form







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type='integer'> 140 </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 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> <power /> <apply> <times /> <cn type='integer'> 38201625 </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'> 512 </cn> <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> <plus /> <apply> <times /> <cn type='integer'> 219520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 583409 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 91803 </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'> 8431 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 280 </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'> 38201625 </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> <times /> <cn type='integer'> 512 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> 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Rule Form





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





2007-05-02