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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=-21/4, b>=a > For fixed z and a=-21/4, b=21/4





http://functions.wolfram.com/07.23.03.a8xj.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 21/4, 5, -z] == (1/(20541646125 Pi z^4)) (4096 (1 + z)^(1/4) (2 (-2688 + 10864 z - 50295 z^2 + 387870 z^3 + 24201265 z^4 + 114302364 z^5 + 224986608 z^6 + 224026880 z^7 + 112062720 z^8 + 22471680 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 2 Sqrt[1 + z] (-1344 + 6440 z - 30135 z^2 + 217350 z^3 + 6918725 z^4 + 24657072 z^5 + 35241360 z^6 + 22865920 z^7 + 5617920 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-2688 + 10864 z - 50295 z^2 + 387870 z^3 + 24201265 z^4 + 114302364 z^5 + 224986608 z^6 + 224026880 z^7 + 112062720 z^8 + 22471680 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