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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=-15/8





http://functions.wolfram.com/07.23.03.b7ko.01









  


  










Input Form





Hypergeometric2F1[-(43/8), -(15/8), 5, z] == (65536 2^(1/4) (-8 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (144942336 - 2613491496 z + 26318923785 z^2 - 250368069105 z^3 - 4962599438740 z^4 - 6204755201586 z^5 - 980533502039 z^6 + 58718141755 z^7 - 4848706590 z^8 + 243960080 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (579769344 - 10671379488 z + 109136483379 z^2 - 1039910304510 z^3 + 18452791498985 z^4 + 56226840030396 z^5 + 24768618377173 z^6 + 59605546546 z^7 - 4894449105 z^8 + 243960080 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (144942336 - 2613491496 z + 26318923785 z^2 - 250368069105 z^3 - 4962599438740 z^4 - 6204755201586 z^5 - 980533502039 z^6 + 58718141755 z^7 - 4848706590 z^8 + 243960080 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 Sqrt[1 - z] (144942336 - 2613491496 z + 26318923785 z^2 - 250368069105 z^3 - 4962599438740 z^4 - 6204755201586 z^5 - 980533502039 z^6 + 58718141755 z^7 - 4848706590 z^8 + 243960080 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1243148557449523725 Pi (1 + Sqrt[1 - z])^(1/4) z^4)










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