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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=1/2, a3>=1/2 > For fixed z and a1=-1/2, a2=1/2, a3=5/2 > For fixed z and a1=-1/2, a2=1/2, a3=5/2, b1=-3/2





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









  


  










Input Form





HypergeometricPFQ[{-(1/2), 1/2, 5/2}, {-(3/2), 2}, -z] == (4 (5 + 11 z + 8 z^2) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (9 Pi z (1 + z)^2) + (4 (5 + 11 z + 8 z^2) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (9 Pi z (1 + z)^(3/2)) + (16 (1 + 2 z) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (9 Pi z (1 + z)^(3/2)) - (8 (7 + 8 z) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (9 Pi z (1 + z))










Standard Form





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MathML Form







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Rule Form





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





2007-05-02