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





http://functions.wolfram.com/07.27.03.6391.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), 1/2, 7/2}, {-(5/2), 2}, -z] == (4 (245 + 1110 z - 704 z^2 + 1792 z^3 - 12288 z^4 - 16384 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1575 Pi z (1 + z)) + (4 (245 + 1110 z - 704 z^2 + 1792 z^3 - 12288 z^4 - 16384 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1575 Pi z Sqrt[1 + z]) + (16 (-455 + 160 z - 384 z^2 + 2048 z^3 + 8192 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(1575 Pi z) - (8 (-665 + 520 z - 1152 z^2 + 5120 z^3 + 8192 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (1575 Pi z Sqrt[1 + z])










Standard Form





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MathML Form







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type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1792 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 704 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1110 </cn> <ci> z </ci> </apply> <cn type='integer'> 245 </cn> </apply> <apply> <ci> EllipticE </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 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-1 </cn> </apply> </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