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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=-9/2, b>=a > For fixed z and a=-9/2, b=17/4





http://functions.wolfram.com/07.23.03.aa57.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 17/4, 4, z] == (Sqrt[2] (2 (1 - z)^(1/4) (-7168 - 36288 z - 260064 z^2 + 10575520 z^3 - 39188640 z^4 + 57280212 z^5 - 37754178 z^6 + 9388071 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-7168 - 36288 z - 260064 z^2 + 10575520 z^3 - 39188640 z^4 + 57280212 z^5 - 37754178 z^6 + 9388071 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (7168 + 36288 z + 260064 z^2 - 10575520 z^3 + 39188640 z^4 - 57280212 z^5 + 37754178 z^6 - 9388071 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (7168 + 36288 z + 260064 z^2 - 10575520 z^3 + 39188640 z^4 - 57280212 z^5 + 37754178 z^6 - 9388071 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (7168 + 36288 z + 260064 z^2 - 10575520 z^3 + 39188640 z^4 - 57280212 z^5 + 37754178 z^6 - 9388071 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (7168 + 32704 z + 241248 z^2 - 4853440 z^3 + 15719840 z^4 - 21201492 z^5 + 13180794 z^6 - 3129357 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (2927925 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