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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 8 and fixed z and a<0 > For fixed z and a=-39/8, b>=a > For fixed z and a=-39/8, b=29/8





http://functions.wolfram.com/07.23.03.bai6.01









  


  










Input Form





Hypergeometric2F1[-(39/8), 29/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-91264 - 254541 z - 1347570 z^2 + 20487775 z^3 - 56271600 z^4 + 66794112 z^5 - 37373952 z^6 + 8110080 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-91264 - 254541 z - 1347570 z^2 + 20487775 z^3 - 56271600 z^4 + 66794112 z^5 - 37373952 z^6 + 8110080 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-91264 - 254541 z - 1347570 z^2 + 20487775 z^3 - 56271600 z^4 + 66794112 z^5 - 37373952 z^6 + 8110080 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-91264 - 220317 z - 1242759 z^2 - 30570155 z^3 + 168173775 z^4 - 338915808 z^5 + 335360256 z^6 - 165040128 z^7 + 32440320 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (52832604825 Pi (1 + Sqrt[1 - z])^(1/4) z^3)










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