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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=-17/4, b>=a > For fixed z and a=-17/4, b=-3/2





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









  


  










Input Form





Hypergeometric2F1[-(17/4), -(3/2), 5, z] == (64 Sqrt[2] (2 (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (113152 - 1640704 z + 12948832 z^2 - 93907320 z^3 - 848794480 z^4 - 490073491 z^5 - 2641408 z^6 + 137984 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-113152 + 1697280 z - 13751504 z^2 + 100134216 z^3 + 2139642220 z^4 + 1922202221 z^5 + 129606400 z^6 - 8259328 z^7 + 413952 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (42748831125 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02