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





http://functions.wolfram.com/07.27.03.9652.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), 7/2, 7/2}, {1/2, 4}, -z] == (1/(225225 Pi z^3)) (32 (-280 - 21 z - 392 z^2 + 53968 z^3 + 697344 z^4 + 1617920 z^5 + 983040 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(225225 Pi z^3)) (32 Sqrt[1 + z] (-280 - 21 z - 392 z^2 + 53968 z^3 + 697344 z^4 + 1617920 z^5 + 983040 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(225225 Pi z^3)) (64 Sqrt[1 + z] (140 - 7 z + 14280 z^2 + 278272 z^3 + 747520 z^4 + 491520 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(225225 Pi z^3)) (256 (-35 - 7 z + 3472 z^2 + 83060 z^3 + 361216 z^4 + 527360 z^5 + 245760 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='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 491520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 747520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 278272 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14280 </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'> 7 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 140 </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'> 225225 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 245760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 527360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 361216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 83060 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3472 </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'> 7 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -35 </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 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Rule Form





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





2007-05-02