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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=-17/4, b>=a > For fixed z and a=-17/4, b=-7/2





http://functions.wolfram.com/07.23.03.aa90.01









  


  










Input Form





Hypergeometric2F1[-(17/4), -(7/2), 3, z] == (Sqrt[2] (2 (-14144 + 484432 z + 43937200 z^2 + 167393180 z^3 + 132608120 z^4 + 21489437 z^5 + 236544 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-14144 + 484432 z + 43937200 z^2 + 167393180 z^3 + 132608120 z^4 + 21489437 z^5 + 236544 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-14144 + 477360 z + 21200720 z^2 + 61287860 z^3 + 35508900 z^4 + 3584227 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-14144 + 484432 z + 43937200 z^2 + 167393180 z^3 + 132608120 z^4 + 21489437 z^5 + 236544 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-14144 + 484432 z + 43937200 z^2 + 167393180 z^3 + 132608120 z^4 + 21489437 z^5 + 236544 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-14144 + 484432 z + 43937200 z^2 + 167393180 z^3 + 132608120 z^4 + 21489437 z^5 + 236544 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (11486475 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