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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=7/4, b>=a > For fixed z and a=7/4, b=15/4





http://functions.wolfram.com/07.23.03.akk6.01









  


  










Input Form





Hypergeometric2F1[7/4, 15/4, -(9/2), z] == (1/(88704 Pi^(3/2))) (((1/(-1 + z)^10) (4 (11088 - 125664 z + 675675 z^2 - 2368135 z^3 + 6691740 z^4 - 25876774 z^5 - 28626853 z^6 - 745875 z^7 + 33150 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^10) (4 (11088 - 125664 z + 675675 z^2 - 2368135 z^3 + 6691740 z^4 - 25876774 z^5 - 28626853 z^6 - 745875 z^7 + 33150 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((-22176 + 11088 Sqrt[z] + 240240 z - 115500 z^(3/2) - 1235850 z^2 + 570185 z^(5/2) + 4166085 z^3 - 1849320 z^(7/2) - 11534160 z^4 + 5014790 z^(9/2) + 46738758 z^5 + 20158856 z^(11/2) + 37094850 z^6 + 1442025 z^(13/2) + 49725 z^7 - 66300 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((22176 + 11088 Sqrt[z] - 240240 z - 115500 z^(3/2) + 1235850 z^2 + 570185 z^(5/2) - 4166085 z^3 - 1849320 z^(7/2) + 11534160 z^4 + 5014790 z^(9/2) - 46738758 z^5 + 20158856 z^(11/2) - 37094850 z^6 + 1442025 z^(13/2) - 49725 z^7 - 66300 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^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