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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=1, b>=a > For fixed z and a=1, b=8/5





http://functions.wolfram.com/07.23.03.az3v.01









  


  










Input Form





Hypergeometric2F1[1, 8/5, 23/5, z] == (936/125) (-5 (1/(3 z^3) + 1/(8 z^2) + 1/(13 z)) - (1/z^(18/5)) (Log[1 - z^(1/5)] + Log[1 - z^(1/5)/E^((2 I Pi)/5)]/ E^((4 I Pi)/5) + E^((4 I Pi)/5) Log[1 - E^((2 I Pi)/5) z^(1/5)] + E^((2 I Pi)/5) Log[1 - z^(1/5)/E^((4 I Pi)/5)] + Log[1 - E^((4 I Pi)/5) z^(1/5)]/E^((2 I Pi)/5))) - (1872/125) (-5 (1/(3 z^2) + 1/(8 z)) - (1/z^(13/5)) (Log[1 - z^(1/5)] + Log[1 - z^(1/5)/E^((2 I Pi)/5)]/E^((4 I Pi)/5) + E^((4 I Pi)/5) Log[1 - E^((2 I Pi)/5) z^(1/5)] + E^((2 I Pi)/5) Log[1 - z^(1/5)/E^((4 I Pi)/5)] + Log[1 - E^((4 I Pi)/5) z^(1/5)]/E^((2 I Pi)/5))) + (936/125) (-(5/(3 z)) - (1/z^(8/5)) (Log[1 - z^(1/5)] + Log[1 - z^(1/5)/E^((2 I Pi)/5)]/E^((4 I Pi)/5) + E^((4 I Pi)/5) Log[1 - E^((2 I Pi)/5) z^(1/5)] + E^((2 I Pi)/5) Log[1 - z^(1/5)/E^((4 I Pi)/5)] + Log[1 - E^((4 I Pi)/5) z^(1/5)]/E^((2 I Pi)/5)))










Standard Form





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MathML Form







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</semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02