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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=5/4, b>=a > For fixed z and a=5/4, b=17/4





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









  


  










Input Form





Hypergeometric2F1[5/4, 17/4, -(9/2), z] == (1/(56160 Pi^(3/2))) (((1/(-1 + z)^10) (2 Sqrt[z] (28080 - 303420 z + 1539759 z^2 - 5020587 z^3 + 12926550 z^4 + 276148830 z^5 + 18675195 z^6 - 2158343 z^7 + 153824 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^10) (2 Sqrt[z] (28080 - 303420 z + 1539759 z^2 - 5020587 z^3 + 12926550 z^4 + 276148830 z^5 + 18675195 z^6 - 2158343 z^7 + 153824 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((-56160 + 84240 Sqrt[z] + 564720 z - 868140 z^(3/2) - 2660190 z^2 + 4199949 z^(5/2) + 8085753 z^3 - 13106340 z^(7/2) - 19963320 z^4 + 32889870 z^(9/2) + 74254830 z^5 + 201894000 z^(11/2) + 17160990 z^6 + 1514205 z^(13/2) - 2042975 z^7 - 115368 z^(15/2) + 153824 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((-56160 - 84240 Sqrt[z] + 564720 z + 868140 z^(3/2) - 2660190 z^2 - 4199949 z^(5/2) + 8085753 z^3 + 13106340 z^(7/2) - 19963320 z^4 - 32889870 z^(9/2) + 74254830 z^5 - 201894000 z^(11/2) + 17160990 z^6 - 1514205 z^(13/2) - 2042975 z^7 + 115368 z^(15/2) + 153824 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