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





http://functions.wolfram.com/07.27.03.3092.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), -(5/2), 5/2}, {1/2, 3}, -z] == -((16 (10 - 85 z - 14763 z^2 + 115457 z^3 - 70403 z^4 + 1200 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2)) - (1/(31185 Pi z^2)) (16 Sqrt[1 + z] (10 - 85 z - 14763 z^2 + 115457 z^3 - 70403 z^4 + 1200 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) - (32 Sqrt[1 + z] (-5 - 3855 z + 63249 z^2 - 106309 z^3 + 28320 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2) + (32 (5 - 3940 z + 48486 z^2 + 9148 z^3 - 42083 z^4 + 1200 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2)










Standard Form





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MathML Form







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/> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1200 </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'> 70403 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 115457 </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'> 14763 </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'> 85 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 10 </cn> </apply> <apply> <ci> EllipticE </ci> 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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 70403 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 115457 </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'> 14763 </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'> 85 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 10 </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> 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type='integer'> 31185 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1200 </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'> 42083 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9148 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 48486 </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'> 3940 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 5 </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'> 31185 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










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





2007-05-02