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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=1/2, a2>=1/2 > For fixed z and a1=1/2, a2=7/2, a3>=7/2 > For fixed z and a1=1/2, a2=7/2, a3=4 > For fixed z and a1=1/2, a2=7/2, a3=4, b1=3





http://functions.wolfram.com/07.27.03.ap3k.01









  


  










Input Form





HypergeometricPFQ[{1/2, 7/2, 4}, {3, 3}, -z] == (8 (-4 + 11 z + 61 z^2 + 40 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(135 Pi z^2 (1 + z)^2) + (8 (-4 + 11 z + 61 z^2 + 40 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(135 Pi z^2 (1 + z)^(3/2)) + (32 (1 + 14 z + 10 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(135 Pi z^2 (1 + z)^(3/2)) - (16 (-2 + 41 z + 40 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(135 Pi z^2 (1 + z))










Standard Form





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MathML Form







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type='integer'> 16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 41 </cn> <ci> z </ci> </apply> <cn type='integer'> -2 </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'> 135 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -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