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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=-9/2





http://functions.wolfram.com/07.23.03.a90w.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(9/2), 3, z] == (2 (1 - z)^(1/4) (-17024 + 740544 z + 57206256 z^2 + 272633600 z^3 + 305730312 z^4 + 88254516 z^5 + 4635771 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-17024 + 740544 z + 57206256 z^2 + 272633600 z^3 + 305730312 z^4 + 88254516 z^5 + 4635771 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-17024 + 740544 z + 57206256 z^2 + 272633600 z^3 + 305730312 z^4 + 88254516 z^5 + 4635771 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-17024 + 740544 z + 57206256 z^2 + 272633600 z^3 + 305730312 z^4 + 88254516 z^5 + 4635771 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-17024 + 740544 z + 57206256 z^2 + 272633600 z^3 + 305730312 z^4 + 88254516 z^5 + 4635771 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (17024 - 749056 z - 9594384 z^2 + 86740528 z^3 + 344124952 z^4 + 261361752 z^5 + 46164951 z^6 + 1118208 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (11810799 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^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