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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Representations through more general functions > Through other functions > Involving some hypergeometric-type functions





http://functions.wolfram.com/06.19.26.0014.01









  


  








Input Form





Beta[z, a, b] == Beta[1, z, a, b] + Beta[a, b] /; Re[b] > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Beta", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Beta", "[", RowBox[List["1", ",", "z", ",", "a", ",", "b"]], "]"]], "+", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "b", "]"]], ">", "0"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CapitalBeta]&quot;, BetaRegularized] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </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> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msub> <semantics> <mi> &#914; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CapitalBeta]&quot;, BetaRegularized] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </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> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Beta", "[", RowBox[List["1", ",", "z", ",", "a", ",", "b"]], "]"]], "+", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "b", "]"]], ">", "0"]]]]]]]]


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





2001-10-29