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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=-17/4, b>=a > For fixed z and a=-17/4, b=19/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), 19/4, -(5/2), z] == (1/(110880 Pi^(3/2))) ((-((1/(-1 + z)^3) (2 (27720 + 144144 z + 825363 z^2 + 10689525 z^3 - 95434880 z^4 + 213596160 z^5 - 188547072 z^6 + 58720256 z^7) EllipticE[(1/2) (1 - Sqrt[z])])) - (1/(-1 + z)^3) (2 (27720 + 144144 z + 825363 z^2 + 10689525 z^3 - 95434880 z^4 + 213596160 z^5 - 188547072 z^6 + 58720256 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2)) ((27720 - 13860 Sqrt[z] + 158004 z - 84777 z^(3/2) + 910140 z^2 - 490875 z^(5/2) + 11180400 z^3 - 25715840 z^(7/2) - 69719040 z^4 + 112097280 z^(9/2) + 101498880 z^5 - 144506880 z^(11/2) - 44040192 z^6 + 58720256 z^(13/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) ((-27720 - 13860 Sqrt[z] - 158004 z - 84777 z^(3/2) - 910140 z^2 - 490875 z^(5/2) - 11180400 z^3 - 25715840 z^(7/2) + 69719040 z^4 + 112097280 z^(9/2) - 101498880 z^5 - 144506880 z^(11/2) + 44040192 z^6 + 58720256 z^(13/2)) 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