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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=11/4, b>=a > For fixed z and a=11/4, b=11/4





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









  


  










Input Form





Hypergeometric2F1[11/4, 11/4, -(9/2), z] == (1/(169344 Pi^(3/2))) ((-((1/(-1 + z)^10) (4 (-21168 + 244608 z - 1350237 z^2 + 4913335 z^3 - 14710570 z^4 + 62862534 z^5 + 88734391 z^6 + 10322051 z^7) EllipticE[(1/2) (1 - Sqrt[z])])) - (1/(-1 + z)^10) (4 (-21168 + 244608 z - 1350237 z^2 + 4913335 z^3 - 14710570 z^4 + 62862534 z^5 + 88734391 z^6 + 10322051 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((-42336 + 21168 Sqrt[z] + 468048 z - 225204 z^(3/2) - 2475270 z^2 + 1144535 z^(5/2) + 8682135 z^3 - 3871700 z^(7/2) - 25549440 z^4 + 11198250 z^(9/2) + 114526818 z^5 + 56680496 z^(11/2) + 120788286 z^6 + 10549927 z^(13/2) + 10094175 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((42336 + 21168 Sqrt[z] - 468048 z - 225204 z^(3/2) + 2475270 z^2 + 1144535 z^(5/2) - 8682135 z^3 - 3871700 z^(7/2) + 25549440 z^4 + 11198250 z^(9/2) - 114526818 z^5 + 56680496 z^(11/2) - 120788286 z^6 + 10549927 z^(13/2) - 10094175 z^7) 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