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





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









  


  








Input Form





HypergeometricPFQ[{-(1/2), 5/2, 5/2}, {5/2, 4}, -z] == (32 (-8 - 5 z + 5 z^2 + 8 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z^3) + (32 Sqrt[1 + z] (-8 - 5 z + 5 z^2 + 8 z^3) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(105 Pi z^3) + (128 Sqrt[1 + z] (2 + z + 2 z^2) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z^3) - (64 (-4 - 3 z + 9 z^2 + 8 z^3) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2])/(105 Pi z^3)








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