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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=-47/8, b>=a > For fixed z and a=-47/8, b=11/8





http://functions.wolfram.com/07.23.03.b56m.01









  


  










Input Form





Hypergeometric2F1[-(47/8), 11/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (1098088448 - 10221659264 z + 41294231349 z^2 - 90938231013 z^3 + 92857305450 z^4 - 174687573354 z^5 + 173755117417 z^6 - 110037009937 z^7 + 44237327784 z^8 - 10347202320 z^9 + 1076712000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (1098088448 - 10221659264 z + 41294231349 z^2 - 90938231013 z^3 + 92857305450 z^4 - 174687573354 z^5 + 173755117417 z^6 - 110037009937 z^7 + 44237327784 z^8 - 10347202320 z^9 + 1076712000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (1098088448 - 10221659264 z + 41294231349 z^2 - 90938231013 z^3 + 92857305450 z^4 - 174687573354 z^5 + 173755117417 z^6 - 110037009937 z^7 + 44237327784 z^8 - 10347202320 z^9 + 1076712000 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (1098088448 - 10907964544 z + 47570171429 z^2 - 115751786073 z^3 + 145918622850 z^4 + 345313337166 z^5 - 517959408743 z^6 + 458826889723 z^7 - 266323796336 z^8 + 99592783680 z^9 - 21878787840 z^10 + 2153424000 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (149532195401844255 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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