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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/06.19.06.0004.02









  


  








Input Form





Beta[z, a, b] \[Proportional] (z^a/a) (1 + O[z]) /; !(Element[-a, Integers] && -a >= 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Beta", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox["z", "a"], "a"], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", "z", "]"]]]], ")"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "a"]], "\[GreaterEqual]", "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> &#8733; </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mi> a </mi> </msup> <mi> a </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8713; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Beta </ci> <ci> z </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <notin /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "a"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", "z", "]"]]]], ")"]]]], "a"], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]]]


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





2001-10-29