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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=-1/4





http://functions.wolfram.com/07.23.03.a9c2.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(1/4), 5, z] == (4096 (-4 (20064 + 20064 Sqrt[z] - 244948 z - 244948 z^(3/2) + 1521520 z^2 + 1521520 z^(5/2) - 7658805 z^3 - 7658805 z^(7/2) - 67762230 z^4 - 67762230 z^(9/2) - 1733082 z^5 - 1733082 z^(11/2) + 429624 z^6 + 429624 z^(13/2) - 76245 z^7 - 76245 z^(15/2) + 6630 z^8 + 6630 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (80256 - 999856 z + 6325385 z^2 - 32090905 z^3 - 35842410 z^4 + 74172462 z^5 - 14658267 z^6 + 3583515 z^7 - 623220 z^8 + 53040 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (466821830475 Pi Sqrt[1 + Sqrt[z]] z^4)










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