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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=-19/4, b>=a > For fixed z and a=-19/4, b=-13/4





http://functions.wolfram.com/07.23.03.a94j.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(13/4), 6, -z] == (1/(94764831586425 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-38912 - 775200 z - 8130537 z^2 - 65315635 z^3 - 579984405 z^4 + 17498228601 z^5 - 33725440875 z^6 + 15456839031 z^7 - 1516424535 z^8 + 480675 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (-38912 - 775200 z - 8130537 z^2 - 65315635 z^3 - 579984405 z^4 + 17498228601 z^5 - 33725440875 z^6 + 15456839031 z^7 - 1516424535 z^8 + 480675 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (38912 + 746016 z + 7575585 z^2 + 59719660 z^3 + 536050515 z^4 - 6325612146 z^5 + 8043576807 z^6 - 2240478720 z^7 + 87963525 z^8 + 961350 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))










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