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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=-15/4, b>=a > For fixed z and a=-15/4, b=7/2





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









  


  








Input Form





Hypergeometric2F1[-(15/4), 7/2, 4, z] == (32 Sqrt[2] (-2 (1 - z)^(1/4) (2464 + 5082 z + 20097 z^2 - 259264 z^3 + 531726 z^4 - 417690 z^5 + 116025 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (2464 + 5082 z + 20097 z^2 - 259264 z^3 + 531726 z^4 - 417690 z^5 + 116025 z^6) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (2464 + 5082 z + 20097 z^2 - 259264 z^3 + 531726 z^4 - 417690 z^5 + 116025 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (2464 + 5082 z + 20097 z^2 - 259264 z^3 + 531726 z^4 - 417690 z^5 + 116025 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (2464 + 5082 z + 20097 z^2 - 259264 z^3 + 531726 z^4 - 417690 z^5 + 116025 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (2464 + 3850 z + 17325 z^2 + 14009 z^3 - 307918 z^4 + 596700 z^5 - 440895 z^6 + 116025 z^7) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (4542615 Pi Sqrt[1 + Sqrt[1 - z]] 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