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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=-5/2





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









  


  










Input Form





Hypergeometric2F1[-(17/4), -(5/2), 5, z] == (32 Sqrt[2] (-2 (17408 - 308992 z + 3064080 z^2 - 28710688 z^3 - 907971340 z^4 - 1448942544 z^5 - 432155119 z^6 - 11038720 z^7 + 236544 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (17408 - 308992 z + 3064080 z^2 - 28710688 z^3 - 907971340 z^4 - 1448942544 z^5 - 432155119 z^6 - 11038720 z^7 + 236544 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-17408 + 300288 z - 2916656 z^2 + 27297920 z^3 + 386826820 z^4 + 444096164 z^5 + 86270481 z^6 + 78848 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (17408 - 308992 z + 3064080 z^2 - 28710688 z^3 - 907971340 z^4 - 1448942544 z^5 - 432155119 z^6 - 11038720 z^7 + 236544 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (17408 - 308992 z + 3064080 z^2 - 28710688 z^3 - 907971340 z^4 - 1448942544 z^5 - 432155119 z^6 - 11038720 z^7 + 236544 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (17408 - 308992 z + 3064080 z^2 - 28710688 z^3 - 907971340 z^4 - 1448942544 z^5 - 432155119 z^6 - 11038720 z^7 + 236544 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (8549766225 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