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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Series representations > Generalized power series > Expansions at z==1 > For the function itself > Logarithmic cases





http://functions.wolfram.com/06.19.06.0048.01









  


  








Input Form





Beta[z, a, b] \[Proportional] (((-1)^(b - 1) Gamma[a])/((-b)! Gamma[a + b])) Log[1 - z] - ((1 - z)^b/b) (1 + (((a - 1) b)/(1 + b)) (z - 1) + (((2 - 3 a + a^2) b)/(2 (2 + b))) (z - 1)^2 + O[(z - 1)^3]) + (Pochhammer[1 - a, -b]/(-b)!) (-EulerGamma - PolyGamma[a] + (1 - a) (z - 1) - (((a - 2) (a - 1))/4) (z - 1)^2 + O[(z - 1)^3]) /; Element[-b - 3, Integers] && -b - 3 >= 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)





2007-05-02