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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=-19/8, b>=a > For fixed z and a=-19/8, b=25/8





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









  


  










Input Form





Hypergeometric2F1[-(19/8), 25/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-6848512 + 21428352 z - 15690675 z^2 - 5778850 z^3 - 5595975 z^4 + 44669100 z^5 - 40768000 z^6 + 11289600 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-6848512 + 23996544 z - 23024067 z^2 - 1719025 z^3 - 2743125 z^4 + 12826905 z^5 - 10721200 z^6 + 2822400 z^7) 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) (-6848512 + 21428352 z - 15690675 z^2 - 5778850 z^3 - 5595975 z^4 + 44669100 z^5 - 40768000 z^6 + 11289600 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-6848512 + 21428352 z - 15690675 z^2 - 5778850 z^3 - 5595975 z^4 + 44669100 z^5 - 40768000 z^6 + 11289600 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (9122984858295 Pi (1 + Sqrt[1 - z])^(1/4) z^5)










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