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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.a8xi.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 21/4, 5, z] == (4096 ((-(2688 + 2688 Sqrt[z] + 10864 z + 10864 z^(3/2) + 50295 z^2 + 50295 z^(5/2) + 387870 z^3 + 387870 z^(7/2) - 24201265 z^4 - 24201265 z^(9/2) + 114302364 z^5 + 114302364 z^(11/2) - 224986608 z^6 - 224986608 z^(13/2) + 224026880 z^7 + 224026880 z^(15/2) - 112062720 z^8 - 112062720 z^(17/2) + 22471680 z^9 + 22471680 z^(19/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 2 (1344 + 5096 z + 23695 z^2 + 187215 z^3 - 7136075 z^4 + 31575797 z^5 - 59898432 z^6 + 58107280 z^7 - 28483840 z^8 + 5617920 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(20541646125 Pi Sqrt[1 + Sqrt[z]] z^4)








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