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http://functions.wolfram.com/06.19.06.0041.01
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Beta[z, a, b] \[Proportional]
Piecewise[{{ComplexInfinity, a == 0 || (Element[-a, Integers] && -a > 0 &&
!(Element[b, Integers] && b > 0 && a + b <= 0))}}, z^a/a] /; (z -> 0)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Beta", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List[RowBox[List["a", "\[Equal]", "0"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "a"]], ">", "0"]], "\[And]", RowBox[List["Not", "[", RowBox[List[RowBox[List["b", "\[Element]", "Integers"]], "\[And]", RowBox[List["b", ">", "0"]], "\[And]", RowBox[List[RowBox[List["a", "+", "b"]], "\[LessEqual]", "0"]]]], "]"]]]], ")"]]]]]], "}"]], "}"]], ",", FractionBox[SuperscriptBox["z", "a"], "a"]]], "]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]
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<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> Β </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> ∝ </mo> <mrow> <mo>  </mo> <mtable> <mtr> <mtd> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mtd> <mtd> <mrow> <mrow> <mi> a </mi> <mo>  </mo> <mn> 0 </mn> </mrow> <mo> ∨ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mo> ¬ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ≤ </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <msup> <mi> z </mi> <mi> a </mi> </msup> <mi> a </mi> </mfrac> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </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> <piecewise> <piece> <apply> <ci> OverTilde </ci> <infinity /> </apply> <apply> <or /> <apply> <eq /> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> b </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <leq /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </piece> <otherwise> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List["ComplexInfinity", RowBox[List[RowBox[List["a", "\[Equal]", "0"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], ">", "0"]], "&&", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]], "&&", RowBox[List[RowBox[List["a", "+", "b"]], "\[LessEqual]", "0"]]]], ")"]]]]]], ")"]]]]], List[FractionBox[SuperscriptBox["z", "a"], "a"], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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