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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=-23/4, b>=a > For fixed z and a=-23/4, b=9/2





http://functions.wolfram.com/07.23.03.a7py.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 9/2, 2, z] == (-2 (1 - z)^(1/4) (38456 - 4775208 z + 43570242 z^2 - 141253799 z^3 + 209862705 z^4 - 146567421 z^5 + 39126945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (38456 - 4775208 z + 43570242 z^2 - 141253799 z^3 + 209862705 z^4 - 146567421 z^5 + 39126945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (38456 - 4775208 z + 43570242 z^2 - 141253799 z^3 + 209862705 z^4 - 146567421 z^5 + 39126945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (38456 - 4775208 z + 43570242 z^2 - 141253799 z^3 + 209862705 z^4 - 146567421 z^5 + 39126945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (38456 - 4775208 z + 43570242 z^2 - 141253799 z^3 + 209862705 z^4 - 146567421 z^5 + 39126945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (38456 - 1160344 z - 1516086 z^2 + 47843593 z^3 - 162857552 z^4 + 232915878 z^5 - 154392810 z^6 + 39126945 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (908523 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)










Standard Form





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MathML Form







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





2007-05-02