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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z1,z2,a,b] > Differentiation > Low-order differentiation > With respect to a





http://functions.wolfram.com/06.20.20.0005.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["a_"]]], RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"], ",", "a_", ",", "b_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["zz", "1"], ",", "a", ",", "b"]], "]"]]]], " ", RowBox[List["Log", "[", SubscriptBox["zz", "1"], "]"]]]], "+", RowBox[List[RowBox[List["Beta", "[", RowBox[List[SubscriptBox["zz", "2"], ",", "a", ",", "b"]], "]"]], " ", RowBox[List["Log", "[", SubscriptBox["zz", "2"], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["Gamma", "[", "a", "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", "a", ",", RowBox[List["1", "-", "b"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "a"]], ",", RowBox[List["1", "+", "a"]]]], "}"]], ",", SubscriptBox["zz", "1"]]], "]"]], " ", SubsuperscriptBox["zz", "1", "a"]]], "-", RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", "a", ",", RowBox[List["1", "-", "b"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "a"]], ",", RowBox[List["1", "+", "a"]]]], "}"]], ",", SubscriptBox["zz", "2"]]], "]"]], " ", SubsuperscriptBox["zz", "2", "a"]]]]], ")"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29