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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[a,b] > Transformations > Multiple arguments





http://functions.wolfram.com/06.18.16.0005.01









  


  








Input Form





Beta[2 a, 2 b] == (Beta[a, b] Beta[a + 1/2, b])/(2^(2 b) Beta[b, b])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Beta", "[", RowBox[List[RowBox[List["2", " ", "a"]], ",", RowBox[List["2", " ", "b"]]]], "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", "b"]]], " ", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], " ", RowBox[List["Beta", "[", RowBox[List[RowBox[List["a", "+", FractionBox["1", "2"]]], ",", "b"]], "]"]]]], RowBox[List["Beta", "[", RowBox[List["b", ",", "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> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> b </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> b </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Beta </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -2 </cn> <ci> b </ci> </apply> </apply> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <ci> Beta </ci> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> b </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List[RowBox[List["2", " ", "a_"]], ",", RowBox[List["2", " ", "b_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", "b"]]], " ", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], " ", RowBox[List["Beta", "[", RowBox[List[RowBox[List["a", "+", FractionBox["1", "2"]]], ",", "b"]], "]"]]]], RowBox[List["Beta", "[", RowBox[List["b", ",", "b"]], "]"]]]]]]]


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





2001-10-29