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





http://functions.wolfram.com/07.23.03.ac3e.01









  


  








Input Form





Hypergeometric2F1[-(7/2), 15/4, 6, z] == (32 Sqrt[2] (-2 (32768 - 82944 z + 18240 z^2 + 21600 z^3 + 55200 z^4 - 431936 z^5 + 633828 z^6 - 377910 z^7 + 82875 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (32768 - 82944 z + 18240 z^2 + 21600 z^3 + 55200 z^4 - 431936 z^5 + 633828 z^6 - 377910 z^7 + 82875 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (32768 - 82944 z + 18240 z^2 + 21600 z^3 + 55200 z^4 - 431936 z^5 + 633828 z^6 - 377910 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (32768 - 82944 z + 18240 z^2 + 21600 z^3 + 55200 z^4 - 431936 z^5 + 633828 z^6 - 377910 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (32768 - 82944 z + 18240 z^2 + 21600 z^3 + 55200 z^4 - 431936 z^5 + 633828 z^6 - 377910 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-32768 + 66560 z + 9920 z^2 - 8800 z^3 - 54400 z^4 - 120224 z^5 + 384540 z^6 - 311610 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (8423415 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








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