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





http://functions.wolfram.com/07.23.03.bj5y.01









  


  










Input Form





Hypergeometric2F1[-(25/8), 19/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-8355840 + 43900800 z - 82792125 z^2 + 49542675 z^3 + 28426125 z^4 - 319877103 z^5 + 353438540 z^6 - 164702720 z^7 + 29352960 z^8) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-8355840 + 47034240 z - 98398125 z^2 + 76543350 z^3 + 16243500 z^4 - 93280278 z^5 + 95426513 z^6 - 42551600 z^7 + 7338240 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-8355840 + 43900800 z - 82792125 z^2 + 49542675 z^3 + 28426125 z^4 - 319877103 z^5 + 353438540 z^6 - 164702720 z^7 + 29352960 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-8355840 + 43900800 z - 82792125 z^2 + 49542675 z^3 + 28426125 z^4 - 319877103 z^5 + 353438540 z^6 - 164702720 z^7 + 29352960 z^8) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (62698383923175 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) 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