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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=-1/2





http://functions.wolfram.com/07.27.03.a9cf.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), -(3/2), 7/2}, {-(1/2), 4}, -z] == -((1/(363825 Pi z^3)) (32 (-280 + 565 z - 2502 z^2 - 55787 z^3 - 360232 z^4 + 40320 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])) - (1/(363825 Pi z^3)) (32 Sqrt[1 + z] (-280 + 565 z - 2502 z^2 - 55787 z^3 - 360232 z^4 + 40320 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (256 Sqrt[1 + z] (35 - 75 z - 5361 z^2 - 31799 z^3 + 60480 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(363825 Pi z^3) + (1/(363825 Pi z^3)) (64 (-140 + 265 z - 23946 z^2 - 182983 z^3 - 118312 z^4 + 40320 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])










Standard Form





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MathML Form







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<times /> <cn type='integer'> 565 </cn> <ci> z </ci> </apply> <cn type='integer'> -280 </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 /> <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'> 363825 </cn> <pi /> <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'> -1 </cn> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 40320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 360232 </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'> 55787 </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'> 2502 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 565 </cn> <ci> z </ci> </apply> <cn type='integer'> -280 </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 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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31799 </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'> 5361 </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'> 75 </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 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type='integer'> 23946 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 265 </cn> <ci> z </ci> </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'> 363825 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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