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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=9/8





http://functions.wolfram.com/07.23.03.b7t7.01









  


  










Input Form





Hypergeometric2F1[-(43/8), 9/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-82824192 + 716946912 z - 2694617145 z^2 + 5469308460 z^3 - 11519887870 z^4 + 12459265692 z^5 - 8641787217 z^6 + 3797513440 z^7 - 966309120 z^8 + 108810240 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-41412096 + 374002992 z - 1477489761 z^2 + 3205393290 z^3 - 1657962590 z^4 + 1723892136 z^5 - 1159231257 z^6 + 496125686 z^7 - 123338880 z^8 + 13601280 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-82824192 + 716946912 z - 2694617145 z^2 + 5469308460 z^3 - 11519887870 z^4 + 12459265692 z^5 - 8641787217 z^6 + 3797513440 z^7 - 966309120 z^8 + 108810240 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-82824192 + 716946912 z - 2694617145 z^2 + 5469308460 z^3 - 11519887870 z^4 + 12459265692 z^5 - 8641787217 z^6 + 3797513440 z^7 - 966309120 z^8 + 108810240 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (328163390911125 Pi (1 + Sqrt[1 - z])^(1/4) z^4)










Standard Form





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MathML Form







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</annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02