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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/06.20.20.0006.01









  


  








Input Form





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








Standard Form





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MathML Form







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Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29