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variants of this functions
BetaRegularized




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.21.20.0004.01









  


  








Input Form





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








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