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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 4 and fixed z > For fixed z and a=-15/4, b>=a > For fixed z and a=-15/4, b=3/2





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









  


  










Input Form





Hypergeometric2F1[-(15/4), 3/2, 4, z] == (64 Sqrt[2] (-2 (1 - z)^(1/4) (6160 - 28875 z + 34650 z^2 - 85588 z^3 + 80322 z^4 - 36504 z^5 + 6630 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (6160 - 28875 z + 34650 z^2 - 85588 z^3 + 80322 z^4 - 36504 z^5 + 6630 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (6160 - 28875 z + 34650 z^2 - 85588 z^3 + 80322 z^4 - 36504 z^5 + 6630 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (6160 - 28875 z + 34650 z^2 - 85588 z^3 + 80322 z^4 - 36504 z^5 + 6630 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (6160 - 28875 z + 34650 z^2 - 85588 z^3 + 80322 z^4 - 36504 z^5 + 6630 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (6160 - 31955 z + 48510 z^2 + 41462 z^3 - 96334 z^4 + 86562 z^5 - 37830 z^6 + 6630 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/(4542615 Pi Sqrt[1 + Sqrt[1 - z]] z^3)










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