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





http://functions.wolfram.com/07.23.03.a9ql.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 17/4, -(11/2), z] == (1/(411840 Pi^(3/2))) (((1/(-1 + z)^5) (2 Sqrt[z] (-205920 + 196560 z + 121914 z^2 + 115167 z^3 + 150228 z^4 + 305955 z^5 - 19201920 z^6 + 41355264 z^7 - 31653888 z^8 + 8388608 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^5) (2 Sqrt[z] (-205920 + 196560 z + 121914 z^2 + 115167 z^3 + 150228 z^4 + 305955 z^5 - 19201920 z^6 + 41355264 z^7 - 31653888 z^8 + 8388608 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((-411840 + 617760 Sqrt[z] + 84240 z - 280800 z^(3/2) + 276120 z^2 - 398034 z^(5/2) + 424437 z^3 - 539604 z^(7/2) + 632502 z^4 - 782730 z^(9/2) + 1126125 z^5 - 1432080 z^(11/2) + 4318080 z^6 + 14883840 z^(13/2) - 23316480 z^7 - 18038784 z^(15/2) + 25362432 z^8 + 6291456 z^(17/2) - 8388608 z^9) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((411840 + 617760 Sqrt[z] - 84240 z - 280800 z^(3/2) - 276120 z^2 - 398034 z^(5/2) - 424437 z^3 - 539604 z^(7/2) - 632502 z^4 - 782730 z^(9/2) - 1126125 z^5 - 1432080 z^(11/2) - 4318080 z^6 + 14883840 z^(13/2) + 23316480 z^7 - 18038784 z^(15/2) - 25362432 z^8 + 6291456 z^(17/2) + 8388608 z^9) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








Standard Form





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MathML Form







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





2007-05-02