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variants of this functions
Beta






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Differentiation > Low-order differentiation > With respect to b





http://functions.wolfram.com/06.19.20.0006.01









  


  










Input Form





D[Beta[z, a, b], {b, 2}] == Beta[a, b] ((PolyGamma[b] - PolyGamma[a + b])^2 + PolyGamma[1, b] - PolyGamma[1, a + b]) - (Beta[1 - z, b, a] Log[1 - z]^2 + 2 (1 - z)^b Gamma[b]^2 (Gamma[b] HypergeometricPFQRegularized[ {b, b, b, 1 - a}, {1 + b, 1 + b, 1 + b}, 1 - z] - HypergeometricPFQRegularized[{b, b, 1 - a}, {1 + b, 1 + b}, 1 - z] Log[1 - z]))










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





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