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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > Specialized values > For fixed b, z





http://functions.wolfram.com/07.23.03.0147.01









  


  








Input Form





Hypergeometric2F1[-n, b, -2 n - 2, z] == ((-(((-1)^n n! Gamma[1 - b])/(2 (2 n + 2)!))) (1/z)^((1 + b + n)/2 - Floor[n/2]) z^((5 + b + 3 n)/2 - Floor[n/2]) ((-(b + 2 n + 2)) LegendreP[n, b + n + 1, 2, 1 - 2/z] + (b + 2 n + 2 - (2 (n + 1))/z) LegendreP[n + 1, b + n + 1, 2, 1 - 2/z]))/ (-1 + z)^((3 + b + n)/2) /; Element[n, Integers] && n >= 0








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