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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=23/4





http://functions.wolfram.com/07.23.03.a7ur.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 23/4, 3, z] == -((1/(422463195 Pi z^2)) (64 Sqrt[1 + Sqrt[z]] ((7084 + 207207 z - 13707543 z^2 + 102509940 z^3 - 297949392 z^4 + 413457408 z^5 - 275808000 z^6 + 71285760 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 4 (1771 - 1771 Sqrt[z] + 53130 z - 53130 z^(3/2) - 86337 z^2 + 86337 z^(5/2) - 10598874 z^3 + 10598874 z^(7/2) + 61124544 z^4 - 61124544 z^(9/2) - 126023040 z^5 + 126023040 z^(11/2) + 111171840 z^6 - 111171840 z^(13/2) - 35642880 z^7 + 35642880 z^(15/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])])))










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