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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==1 > For the function itself > Generic formulas for main term





http://functions.wolfram.com/07.24.06.0063.01









  


  










Input Form





Hypergeometric2F1Regularized[a, b, c, z] \[Proportional] Piecewise[{{0, Element[-c, Integers] && -c >= 0 && ((Element[-a, Integers] && -a >= 0 && c - a <= 0) && (Element[-b, Integers] && -b >= 0 && c - b <= 0))}, {Gamma[c - a - b]/(Gamma[c - a] Gamma[c - b]), Re[c - a - b] > 0}, {(Gamma[a + b - c]/(Gamma[a] Gamma[b])) (1 - z)^(c - a - b), Re[c - a - b] < 0}, {-(Log[1 - z]/(Gamma[a] Gamma[b])), c == a + b}}, Gamma[c - a - b]/(Gamma[c - a] Gamma[c - b]) + (Gamma[a + b - c]/(Gamma[a] Gamma[b])) (1 - z)^(c - a - b)] /; (z -> 1)










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)





2007-05-02





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