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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 5 and fixed z > For fixed z and a=-21/5, b>=a > For fixed z and a=-21/5, b=6





http://functions.wolfram.com/07.23.03.ar11.01









  


  








Input Form





Hypergeometric2F1[-(21/5), 6, -(6/5), z] == (1/1953125) (308 ((125 (3643 - 6966 z + 3348 z^2))/(-1 + z)^3 - 2437344 ((-(5/66)) (6 + 11 z + 66 z^2) - z^(11/5) (Log[1 - z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)])) + 12491388 ((-(5/528)) (33 + 48 z + 88 z^2 + 528 z^3) - z^(16/5) (Log[1 - z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)])) - 13681044 (-(5/21) - (5 z)/16 - (5 z^2)/11 - (5 z^3)/6 - 5 z^4 - z^(21/5) (Log[1 - z^(1/5)] - (-1)^(1/5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)]))))








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