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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=-23/4, b>=a > For fixed z and a=-23/4, b=17/4





http://functions.wolfram.com/07.23.03.9965.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 17/4, -(7/2), z] == (1/(109200 Pi^(3/2))) (((1/(-1 + z)^2) (8 Sqrt[z] (13650 + 73125 z + 327015 z^2 + 1750125 z^3 - 331673088 z^4 + 1180784640 z^5 - 1379926016 z^6 + 528482304 z^7) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^2) (8 Sqrt[z] (13650 + 73125 z + 327015 z^2 + 1750125 z^3 - 331673088 z^4 + 1180784640 z^5 - 1379926016 z^6 + 528482304 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z]))) ((109200 - 163800 Sqrt[z] + 666900 z - 959400 z^(3/2) + 3124485 z^2 - 4432545 z^(5/2) + 16399500 z^3 - 23400000 z^(7/2) + 179712000 z^4 + 1146980352 z^(9/2) - 2020171776 z^5 - 2702966784 z^(11/2) + 3934257152 z^6 + 1585446912 z^(13/2) - 2113929216 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/(-1 - Sqrt[z] + z + z^(3/2))) ((-109200 - 163800 Sqrt[z] - 666900 z - 959400 z^(3/2) - 3124485 z^2 - 4432545 z^(5/2) - 16399500 z^3 - 23400000 z^(7/2) - 179712000 z^4 + 1146980352 z^(9/2) + 2020171776 z^5 - 2702966784 z^(11/2) - 3934257152 z^6 + 1585446912 z^(13/2) + 2113929216 z^7) 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