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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=7/2





http://functions.wolfram.com/07.23.03.a8rg.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 7/2, 3, z] == (8 Sqrt[2] (-2 (37128 + 408408 z - 23746181 z^2 + 120474105 z^3 - 251027050 z^4 + 261683466 z^5 - 135975609 z^6 + 28164213 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (37128 + 408408 z - 23746181 z^2 + 120474105 z^3 - 251027050 z^4 + 261683466 z^5 - 135975609 z^6 + 28164213 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-37128 - 426972 z + 10909175 z^2 - 39382820 z^3 + 57268850 z^4 - 37725336 z^5 + 9388071 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (37128 + 408408 z - 23746181 z^2 + 120474105 z^3 - 251027050 z^4 + 261683466 z^5 - 135975609 z^6 + 28164213 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (37128 + 408408 z - 23746181 z^2 + 120474105 z^3 - 251027050 z^4 + 261683466 z^5 - 135975609 z^6 + 28164213 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (37128 + 408408 z - 23746181 z^2 + 120474105 z^3 - 251027050 z^4 + 261683466 z^5 - 135975609 z^6 + 28164213 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (50470875 Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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