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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=-17/4, b>=a > For fixed z and a=-17/4, b=1/4





http://functions.wolfram.com/07.23.03.aai2.01









  


  










Input Form





Hypergeometric2F1[-(17/4), 1/4, 5, -z] == (1/(128246493375 Pi z^4)) (4096 (1 + z)^(1/4) (2 (-84864 - 859248 z - 4206735 z^2 - 15169440 z^3 + 60579750 z^4 + 18399612 z^5 + 5953409 z^6 + 1279740 z^7 + 129360 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 4 Sqrt[1 + z] (-21216 - 198900 z - 904995 z^2 - 3135990 z^3 + 1744050 z^4 + 611688 z^5 + 145145 z^6 + 16170 z^7) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-84864 - 859248 z - 4206735 z^2 - 15169440 z^3 + 60579750 z^4 + 18399612 z^5 + 5953409 z^6 + 1279740 z^7 + 129360 z^8) 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