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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=-11/2, b>=a > For fixed z and a=-11/2, b=7/4





http://functions.wolfram.com/07.23.03.a80v.01









  


  










Input Form





Hypergeometric2F1[-(11/2), 7/4, 4, z] == (-2 (473088 - 2454144 z + 2069760 z^2 - 12303680 z^3 + 22489120 z^4 - 22494536 z^5 + 13138008 z^6 - 4223310 z^7 + 580125 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (473088 - 2454144 z + 2069760 z^2 - 12303680 z^3 + 22489120 z^4 - 22494536 z^5 + 13138008 z^6 - 4223310 z^7 + 580125 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (473088 - 2217600 z + 1034880 z^2 + 3219520 z^3 - 10828320 z^4 + 14361464 z^5 - 10130640 z^6 + 3759210 z^7 - 580125 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (473088 - 2454144 z + 2069760 z^2 - 12303680 z^3 + 22489120 z^4 - 22494536 z^5 + 13138008 z^6 - 4223310 z^7 + 580125 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (473088 - 2454144 z + 2069760 z^2 - 12303680 z^3 + 22489120 z^4 - 22494536 z^5 + 13138008 z^6 - 4223310 z^7 + 580125 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (473088 - 2454144 z + 2069760 z^2 - 12303680 z^3 + 22489120 z^4 - 22494536 z^5 + 13138008 z^6 - 4223310 z^7 + 580125 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (3828825 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02