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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Specific values > Specialized values > For fixed z,b





http://functions.wolfram.com/06.19.03.0002.01









  


  








Input Form





Beta[z, -n, b] == ComplexInfinity /; n == 0 || (Element[n, Integers] && n > 0 && !(Element[b, Integers] && b > 0 && b <= n))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Beta", "[", RowBox[List["z", ",", RowBox[List["-", "n"]], ",", "b"]], "]"]], "\[Equal]", InterpretationBox["ComplexInfinity", DirectedInfinity[]]]], "/;", RowBox[List[RowBox[List["n", "\[Equal]", "0"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List["b", "\[Element]", "Integers"]], "\[And]", RowBox[List["b", ">", "0"]], "\[And]", RowBox[List["b", "\[LessEqual]", "n"]]]], "]"]]]], ")"]]]]]]]]








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> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> b </mi> <mo> &#8804; </mo> <mi> n </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Beta </ci> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <ci> b </ci> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <apply> <or /> <apply> <eq /> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> b </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <leq /> <ci> b </ci> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List["z_", ",", RowBox[List["-", "n_"]], ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ComplexInfinity", "/;", RowBox[List[RowBox[List["n", "\[Equal]", "0"]], "||", RowBox[List["(", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]], "&&", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]], "&&", RowBox[List["b", "\[LessEqual]", "n"]]]], ")"]]]]]], ")"]]]]]]]]]]


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





2001-10-29