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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-13/4, b>=a > For fixed z and a=-13/4, b=3/4





http://functions.wolfram.com/07.23.03.acfj.01









  


  










Input Form





Hypergeometric2F1[-(13/4), 3/4, -(7/2), z] == (1/(6720 Pi^(3/2))) (((2 (-1680 + 300 z + 203 z^2 + 208 z^3 + 384 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z) + (2 (-1680 + 300 z + 203 z^2 + 208 z^3 + 384 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z) + (1/(-1 + Sqrt[z])) ((1680 - 840 Sqrt[z] + 540 z - 620 z^(3/2) + 417 z^2 - 496 z^(5/2) + 288 z^3 - 384 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/(1 + Sqrt[z])) ((1680 + 840 Sqrt[z] + 540 z + 620 z^(3/2) + 417 z^2 + 496 z^(5/2) + 288 z^3 + 384 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










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