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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/07.24.03.0210.01









  


  








Input Form





Hypergeometric2F1Regularized[1, 1/2 - n, 3/2, z] == (((2 n - 1)!! (1 - z)^n)/((2 n)!! Sqrt[Pi] Sqrt[z])) Log[(1 + Sqrt[z])/(1 - Sqrt[z])] + ((2 (1 - z)^n)/(z Sqrt[Pi])) Sum[(((2 n - 1)!! (k - 1)!)/(2^(n - k + 1) n!)) Sum[(((-1)^(k - j) Binomial[n, j] (2 j - 2 k - 1)!!)/(2 j - 1)!!) (z/(1 - z))^k, {j, k, n}], {k, 1, n}] /; Element[n, {1, 2}]








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