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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=-21/8, b>=a > For fixed z and a=-21/8, b=-1/8





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









  


  










Input Form





Hypergeometric2F1[-(21/8), -(1/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-2981888 + 28898688 z - 130516113 z^2 + 379335320 z^3 - 928885230 z^4 - 6539213580 z^5 - 18055785 z^6 + 1380060 z^7) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-2981888 + 28898688 z - 130516113 z^2 + 379335320 z^3 - 928885230 z^4 - 6539213580 z^5 - 18055785 z^6 + 1380060 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-2981888 + 28898688 z - 130516113 z^2 + 379335320 z^3 - 928885230 z^4 - 6539213580 z^5 - 18055785 z^6 + 1380060 z^7) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-2981888 + 30016896 z - 141047361 z^2 + 425478053 z^3 - 1059220890 z^4 + 8503050 z^5 + 808600155 z^6 - 74868255 z^7 + 5520240 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (1633714091284275 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