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variants of this functions
BetaRegularized




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > BetaRegularized[z,a,b] > Identities > Functional identities > Relations between contiguous functions





http://functions.wolfram.com/06.21.17.0005.01









  


  








Input Form





BetaRegularized[z, a, b] == (1/(a + b)) (a BetaRegularized[z, a + 1, b] + b BetaRegularized[z, a, b + 1])








Standard Form





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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BetaRegularized", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["a", " ", RowBox[List["BetaRegularized", "[", RowBox[List["z", ",", RowBox[List["a", "+", "1"]], ",", "b"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["BetaRegularized", "[", RowBox[List["z", ",", "a", ",", RowBox[List["b", "+", "1"]]]], "]"]]]]]], RowBox[List["a", "+", "b"]]]]]]]


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





2001-10-29