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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Case of simple poles





http://functions.wolfram.com/07.24.06.0021.02









  


  










Input Form





Hypergeometric2F1Regularized[a, b, c, z] \[Proportional] ((Gamma[b - a]/(Gamma[b] Gamma[c - a])) (1 + (a (1 + a - c))/((1 + a - b) z) + (a (1 + a) (1 + a - c) (2 + a - c))/(2 (1 + a - b) (2 + a - b) z^2) + \[Ellipsis]))/(-z)^a + ((Gamma[a - b]/(Gamma[a] Gamma[c - b])) (1 + (b (1 + b - c))/((1 - a + b) z) + (b (1 + b) (1 + b - c) (2 + b - c))/(2 (1 - a + b) (2 - a + b) z^2) + \[Ellipsis]))/(-z)^b /; (Abs[z] -> Infinity) && !Element[a - b, Integers]










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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