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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=23/4





http://functions.wolfram.com/07.23.03.ac5o.01









  


  








Input Form





Hypergeometric2F1[-(7/2), 23/4, 6, z] == (32 Sqrt[2] (-2 (32768 + 56320 z + 122688 z^2 + 358880 z^3 + 1806880 z^4 - 28372320 z^5 + 64112100 z^6 - 54027870 z^7 + 15862275 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (32768 + 56320 z + 122688 z^2 + 358880 z^3 + 1806880 z^4 - 28372320 z^5 + 64112100 z^6 - 54027870 z^7 + 15862275 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (32768 + 56320 z + 122688 z^2 + 358880 z^3 + 1806880 z^4 - 28372320 z^5 + 64112100 z^6 - 54027870 z^7 + 15862275 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (32768 + 56320 z + 122688 z^2 + 358880 z^3 + 1806880 z^4 - 28372320 z^5 + 64112100 z^6 - 54027870 z^7 + 15862275 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (32768 + 56320 z + 122688 z^2 + 358880 z^3 + 1806880 z^4 - 28372320 z^5 + 64112100 z^6 - 54027870 z^7 + 15862275 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-32768 - 72704 z - 164160 z^2 - 454880 z^3 - 2067200 z^4 - 2758080 z^5 + 31041660 z^6 - 41338050 z^7 + 15862275 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (480134655 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