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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=-43/8, b>=a > For fixed z and a=-43/8, b=39/8





http://functions.wolfram.com/07.23.03.b87p.01









  


  










Input Form





Hypergeometric2F1[-(43/8), 39/8, 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-2650374144 + 735064704 z + 1167060807 z^2 + 3118444065 z^3 + 16454918403 z^4 - 363522541205 z^5 + 1203567730330 z^6 - 1807698074960 z^7 + 1437887349600 z^8 - 592597674240 z^9 + 100164979200 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (165648384 + 74412360 z - 7198587 z^2 - 189185337 z^3 - 108526787325 z^4 + 442106728505 z^5 - 743842357600 z^6 + 640988700560 z^7 - 281274090240 z^8 + 50082489600 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (331296768 - 37529712 z - 135479025 z^2 - 405304713 z^3 + 126714138705 z^4 - 588055710755 z^5 + 1182425357260 z^6 - 1300257654800 z^7 + 819137879040 z^8 - 279108360960 z^9 + 40065991680 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-2650374144 + 735064704 z + 1167060807 z^2 + 3118444065 z^3 + 16454918403 z^4 - 363522541205 z^5 + 1203567730330 z^6 - 1807698074960 z^7 + 1437887349600 z^8 - 592597674240 z^9 + 100164979200 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (168872880962864925 Pi z^5)










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