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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=19/8





http://functions.wolfram.com/07.23.03.b5b8.01









  


  










Input Form





Hypergeometric2F1[-(47/8), 19/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-1098088448 + 7236231296 z - 17130923733 z^2 + 10795233540 z^3 + 18571461090 z^4 - 91236216876 z^5 + 142834918667 z^6 - 123026667056 z^7 + 62492364480 z^8 - 17658076800 z^9 + 2153424000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-1098088448 + 7236231296 z - 17130923733 z^2 + 10795233540 z^3 + 18571461090 z^4 - 91236216876 z^5 + 142834918667 z^6 - 123026667056 z^7 + 62492364480 z^8 - 17658076800 z^9 + 2153424000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-1098088448 + 7236231296 z - 17130923733 z^2 + 10795233540 z^3 + 18571461090 z^4 - 91236216876 z^5 + 142834918667 z^6 - 123026667056 z^7 + 62492364480 z^8 - 17658076800 z^9 + 2153424000 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-1098088448 + 7922536576 z - 21540971333 z^2 + 20812844325 z^3 + 13265329350 z^4 + 113049855114 z^5 - 315500491033 z^6 + 407567659409 z^7 - 310716267160 z^8 + 143881024560 z^9 - 37684920000 z^10 + 4306848000 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (56719108600699545 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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