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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=-5/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), -(5/4), 11/2, z] == (1/(45128457297 Pi^(3/2) z^(9/2))) (8 (2 Sqrt[z] (-26520 + 371280 z - 2669901 z^2 + 14818713 z^3 + 1290775302 z^4 + 1079828034 z^5 + 35499695 z^6 - 2831323 z^7 + 153824 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-26520 + 371280 z - 2669901 z^2 + 14818713 z^3 + 1290775302 z^4 + 1079828034 z^5 + 35499695 z^6 - 2831323 z^7 + 153824 z^8) EllipticE[(1/2) (1 + Sqrt[z])] - (53040 - 26520 Sqrt[z] - 782340 z + 371280 z^(3/2) + 5890755 z^2 - 2669901 z^(5/2) - 33561723 z^3 + 14818713 z^(7/2) + 260645190 z^4 + 1290775302 z^(9/2) + 1446241926 z^5 + 1079828034 z^(11/2) + 738090815 z^6 + 35499695 z^(13/2) - 697015 z^7 - 2831323 z^(15/2) + 38456 z^8 + 153824 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])] - (-53040 - 26520 Sqrt[z] + 782340 z + 371280 z^(3/2) - 5890755 z^2 - 2669901 z^(5/2) + 33561723 z^3 + 14818713 z^(7/2) - 260645190 z^4 + 1290775302 z^(9/2) - 1446241926 z^5 + 1079828034 z^(11/2) - 738090815 z^6 + 35499695 z^(13/2) + 697015 z^7 - 2831323 z^(15/2) - 38456 z^8 + 153824 z^(17/2)) 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