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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z1,z2,a,b] > Integration > Indefinite integration > Involving one direct function and elementary functions with respect to z1 > Involving power function





http://functions.wolfram.com/06.20.21.0008.01









  


  








Input Form





Integrate[Subscript[z, 2]^(\[Alpha] - 1) Beta[Subscript[z, 1], Subscript[z, 2], a, b], Subscript[z, 2]] == (1/\[Alpha]) (Subscript[z, 2]^\[Alpha] Beta[Subscript[z, 1], Subscript[z, 2], a, b] - Beta[Subscript[z, 2], \[Alpha] + a, b])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SubsuperscriptBox["z", "2", RowBox[List["\[Alpha]", "-", "1"]]], RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"], ",", "a", ",", "b"]], "]"]], RowBox[List["\[DifferentialD]", SubscriptBox["z", "2"]]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "\[Alpha]"], RowBox[List["(", RowBox[List[RowBox[List[SubsuperscriptBox["z", "2", "\[Alpha]"], " ", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z", RowBox[List[" ", "1"]]], ",", SubscriptBox["z", RowBox[List[" ", "2"]]], ",", "a", ",", "b"]], "]"]]]], "-", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z", RowBox[List[" ", "2"]]], ",", RowBox[List["\[Alpha]", "+", "a"]], ",", "b"]], "]"]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <msubsup> <mi> z </mi> <mn> 2 </mn> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CapitalBeta]&quot;, BetaRegularized] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> &#945; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msubsup> <mi> z </mi> <mn> 2 </mn> <mi> &#945; </mi> </msubsup> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CapitalBeta]&quot;, BetaRegularized] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> &#945; </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <msubsup> <mi> z </mi> <mn> 2 </mn> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CapitalBeta]&quot;, BetaRegularized] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> &#945; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msubsup> <mi> z </mi> <mn> 2 </mn> <mi> &#945; </mi> </msubsup> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CapitalBeta]&quot;, BetaRegularized] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> &#945; </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SubsuperscriptBox["z_", "2", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"], ",", "a_", ",", "b_"]], "]"]]]], RowBox[List["\[DifferentialD]", SubscriptBox["z_", "2"]]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SubsuperscriptBox["zz", "2", "\[Alpha]"], " ", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"], ",", "a", ",", "b"]], "]"]]]], "-", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["\[Alpha]", "+", "a"]], ",", "b"]], "]"]]]], "\[Alpha]"]]]]]


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





2001-10-29