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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=-47/8, b>=a > For fixed z and a=-47/8, b=-37/8





http://functions.wolfram.com/07.23.03.b4np.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(37/8), 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (59832952192 - 1991782885079 z + 51728859284557 z^2 + 2691565757987285 z^3 + 11726915063055545 z^4 + 13701319267397675 z^5 + 4757606164882935 z^6 + 387791736813975 z^7 + 725838098115 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (59832952192 - 1991782885079 z + 51728859284557 z^2 + 2691565757987285 z^3 + 11726915063055545 z^4 + 13701319267397675 z^5 + 4757606164882935 z^6 + 387791736813975 z^7 + 725838098115 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (59832952192 - 1991782885079 z + 51728859284557 z^2 + 2691565757987285 z^3 + 11726915063055545 z^4 + 13701319267397675 z^5 + 4757606164882935 z^6 + 387791736813975 z^7 + 725838098115 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (59832952192 - 2029178480199 z + 52967588372907 z^2 - 2786706623566505 z^3 - 26700716409937545 z^4 - 57463452285847395 z^5 - 38383779053651135 z^6 - 7678004009473395 z^7 - 302674486913955 z^8 + 1451676196230 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5576850641068782075 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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