Directed infinity: Transformations (formula 02.13.16.0012)

DirectedInfinity

$Mathematica Notation$

Constants

DirectedInfinity[z]

Transformations

Products, sums, and powers of the direct function

Products involving the direct function

http://functions.wolfram.com/02.13.16.0012.01

Input Form

a DirectedInfinity[z] == DirectedInfinity[-Sign[z]] /; a < 0

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List["DirectedInfinity", "[", "z", "]"]]]], "\[Equal]", RowBox[List["DirectedInfinity", "[", RowBox[List["-", RowBox[List["Sign", "[", "z", "]"]]]], "]"]]]], "/;", RowBox[List["a", "<", "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> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mi> ∞ </mi> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> a </mi> <mo> < </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <ci> a </ci> <apply> <times /> <ci> z </ci> <infinity /> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Sign </ci> <ci> z </ci> </apply> </apply> <infinity /> </apply> </apply> <apply> <lt /> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["a_", " ", RowBox[List["DirectedInfinity", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DirectedInfinity", "[", RowBox[List["-", RowBox[List["Sign", "[", "z", "]"]]]], "]"]], "/;", RowBox[List["a", "<", "0"]]]]]]]]

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

2001-10-29