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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[a,b] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/06.18.27.0002.01









  


  








Input Form





Beta[a, b] == ((a - 1)! (b - 1)!)/(a + b - 1)!








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "1"]], ")"]], "!"]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]], "!"]]]]]]]








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> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <times /> <apply> <factorial /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </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["a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "1"]], ")"]], "!"]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]], "!"]]]]]]]


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





2001-10-29