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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=-11/4





http://functions.wolfram.com/07.23.03.a95h.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(11/4), 11/2, z] == (1/(569919523875 Pi^(3/2) z^(9/2))) (32 (2 (-491568 + 9357348 z - 95985967 z^2 + 810019210 z^3 - 10814693505 z^4 - 66880161116 z^5 - 64622531329 z^6 - 12909262134 z^7 - 117765375 z^8 + 2691780 z^9) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-491568 + 9357348 z - 95985967 z^2 + 810019210 z^3 - 10814693505 z^4 - 66880161116 z^5 - 64622531329 z^6 - 12909262134 z^7 - 117765375 z^8 + 2691780 z^9) EllipticE[(1/2) (1 + Sqrt[z])] - (-491568 - 245784 Sqrt[z] + 9357348 z + 4658192 z^(3/2) - 95985967 z^2 - 47613335 z^(5/2) + 810019210 z^3 + 401198490 z^(7/2) - 10814693505 z^4 - 23185459145 z^(9/2) - 66880161116 z^5 - 73947492868 z^(11/2) - 64622531329 z^6 - 50497327641 z^(13/2) - 12909262134 z^7 - 7347213510 z^(15/2) - 117765375 z^8 + 672945 z^(17/2) + 2691780 z^9) EllipticK[(1/2) (1 - Sqrt[z])] + (-491568 + 245784 Sqrt[z] + 9357348 z - 4658192 z^(3/2) - 95985967 z^2 + 47613335 z^(5/2) + 810019210 z^3 - 401198490 z^(7/2) - 10814693505 z^4 + 23185459145 z^(9/2) - 66880161116 z^5 + 73947492868 z^(11/2) - 64622531329 z^6 + 50497327641 z^(13/2) - 12909262134 z^7 + 7347213510 z^(15/2) - 117765375 z^8 - 672945 z^(17/2) + 2691780 z^9) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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