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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.aaln.01









  


  








Input Form





Hypergeometric2F1[-(17/4), 3/2, 5, z] == (512 Sqrt[2] (2 (42432 - 286416 z + 759135 z^2 - 742560 z^3 + 3026200 z^4 - 3322336 z^5 + 1984928 z^6 - 640640 z^7 + 87780 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (42432 - 286416 z + 759135 z^2 - 742560 z^3 + 3026200 z^4 - 3322336 z^5 + 1984928 z^6 - 640640 z^7 + 87780 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-42432 + 265200 z - 633165 z^2 + 464100 z^3 - 705700 z^4 + 509756 z^5 - 189860 z^6 + 29260 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (42432 - 286416 z + 759135 z^2 - 742560 z^3 + 3026200 z^4 - 3322336 z^5 + 1984928 z^6 - 640640 z^7 + 87780 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (42432 - 286416 z + 759135 z^2 - 742560 z^3 + 3026200 z^4 - 3322336 z^5 + 1984928 z^6 - 640640 z^7 + 87780 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (42432 - 286416 z + 759135 z^2 - 742560 z^3 + 3026200 z^4 - 3322336 z^5 + 1984928 z^6 - 640640 z^7 + 87780 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (555179625 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