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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=1/4, b>=a > For fixed z and a=1/4, b=17/4





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









  


  










Input Form





Hypergeometric2F1[1/4, 17/4, -(9/2), z] == (1/(56160 Pi^(3/2))) (((1/(-1 + z)^9) (2 Sqrt[z] (-28080 + 248820 z - 985959 z^2 + 2316132 z^3 - 3678090 z^4 - 8778000 z^5 + 3182025 z^6 - 745712 z^7 + 80256 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^9) (2 Sqrt[z] (-28080 + 248820 z - 985959 z^2 + 2316132 z^3 - 3678090 z^4 - 8778000 z^5 + 3182025 z^6 - 745712 z^7 + 80256 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((-56160 + 84240 Sqrt[z] + 455520 z - 704340 z^(3/2) - 1634490 z^2 + 2620449 z^(5/2) + 3437928 z^3 - 5754060 z^(7/2) - 4880460 z^4 + 8558550 z^(9/2) + 6846840 z^5 + 1931160 z^(11/2) - 2677290 z^6 - 504735 z^(13/2) + 685520 z^7 + 60192 z^(15/2) - 80256 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((56160 + 84240 Sqrt[z] - 455520 z - 704340 z^(3/2) + 1634490 z^2 + 2620449 z^(5/2) - 3437928 z^3 - 5754060 z^(7/2) + 4880460 z^4 + 8558550 z^(9/2) - 6846840 z^5 + 1931160 z^(11/2) + 2677290 z^6 - 504735 z^(13/2) - 685520 z^7 + 60192 z^(15/2) + 80256 z^8) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^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