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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Specific values > Specialized values > For fixed z and integer parameters





http://functions.wolfram.com/07.24.03.0172.01









  


  










Input Form





Hypergeometric2F1Regularized[1, m/n, m/n + 1, z] == ((-(1/Gamma[m/n])) (Log[1 - z^(1/n)] + (((-1)^m (1 + (-1)^n))/2) Log[1 + z^(1/n)] + Sum[Cos[(2 Pi k m)/n] Log[1 - 2 z^(1/n) Cos[(2 Pi k)/n] + z^(2/n)] - 2 Sin[(2 Pi k m)/n] ArcTan[(z^(1/n) Sin[(2 Pi k)/n])/ (1 - z^(1/n) Cos[(2 Pi k)/n])], {k, 1, Floor[(n - 1)/2]}]))/ z^(m/n) /; Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0 && n > m










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)





2001-10-29





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