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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=5/2





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









  


  








Input Form





Hypergeometric2F1[-(13/4), 5/2, 6, z] == (2048 Sqrt[2] (-2 (-19968 + 100464 z - 174915 z^2 + 79170 z^3 + 68250 z^4 - 473586 z^5 + 519838 z^6 - 244090 z^7 + 43890 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-19968 + 100464 z - 174915 z^2 + 79170 z^3 + 68250 z^4 - 473586 z^5 + 519838 z^6 - 244090 z^7 + 43890 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (19968 - 90480 z + 132795 z^2 - 25350 z^3 - 66300 z^4 + 117906 z^5 - 69520 z^6 + 14630 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-19968 + 100464 z - 174915 z^2 + 79170 z^3 + 68250 z^4 - 473586 z^5 + 519838 z^6 - 244090 z^7 + 43890 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-19968 + 100464 z - 174915 z^2 + 79170 z^3 + 68250 z^4 - 473586 z^5 + 519838 z^6 - 244090 z^7 + 43890 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-19968 + 100464 z - 174915 z^2 + 79170 z^3 + 68250 z^4 - 473586 z^5 + 519838 z^6 - 244090 z^7 + 43890 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (333107775 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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





2007-05-02