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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=-21/4, b>=a > For fixed z and a=-21/4, b=1/2





http://functions.wolfram.com/07.23.03.a8i6.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 1/2, 4, z] == (32 Sqrt[2] (-2 (-148512 + 1512966 z - 8144955 z^2 - 36909520 z^3 + 26186800 z^4 - 15700224 z^5 + 6449872 z^6 - 1586200 z^7 + 175560 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-148512 + 1512966 z - 8144955 z^2 - 36909520 z^3 + 26186800 z^4 - 15700224 z^5 + 6449872 z^6 - 1586200 z^7 + 175560 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (148512 - 1438710 z + 7448805 z^2 + 5722000 z^3 - 3833600 z^4 + 1763904 z^5 - 481360 z^6 + 58520 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-148512 + 1512966 z - 8144955 z^2 - 36909520 z^3 + 26186800 z^4 - 15700224 z^5 + 6449872 z^6 - 1586200 z^7 + 175560 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-148512 + 1512966 z - 8144955 z^2 - 36909520 z^3 + 26186800 z^4 - 15700224 z^5 + 6449872 z^6 - 1586200 z^7 + 175560 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-148512 + 1512966 z - 8144955 z^2 - 36909520 z^3 + 26186800 z^4 - 15700224 z^5 + 6449872 z^6 - 1586200 z^7 + 175560 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (555179625 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