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variants of this functions
Beta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.20.20.0014.01









  


  










Input Form





D[Beta[Subscript[z, 1], Subscript[z, 2], a, b], {Subscript[z, 1], \[Alpha]}] == Beta[Subscript[z, 2], a, b] (1/(Subscript[z, 1]^\[Alpha] Gamma[1 - \[Alpha]])) - Subscript[z, 1]^(a - \[Alpha]) Gamma[a] HypergeometricPFQRegularized[{a, 1 - b}, {1 + a - \[Alpha]}, Subscript[z, 1]] /; !(Element[-a, Integers] && -a > 0)










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[RowBox[List["{", RowBox[List[SubscriptBox["z_", "1"], ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"], ",", "a_", ",", "b_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Beta", "[", RowBox[List[SubscriptBox["zz", "2"], ",", "a", ",", "b"]], "]"]], " ", SubsuperscriptBox["zz", "1", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]], "-", RowBox[List[SubsuperscriptBox["zz", "1", RowBox[List["a", "-", "\[Alpha]"]]], " ", RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", RowBox[List["1", "-", "b"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "a", "-", "\[Alpha]"]], "}"]], ",", SubscriptBox["zz", "1"]]], "]"]]]]]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], ">", "0"]]]], ")"]]]]]]]]]]










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





2001-10-29