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http://functions.wolfram.com/14.01.17.0001.01
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UnitStep[a x + b] == UnitStep[x + b/a] UnitStep[a] +
UnitStep[-x - b/a] UnitStep[-a] /; Element[a, Reals] && Element[b, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["a", " ", "x"]], "+", "b"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["x", "+", FractionBox["b", "a"]]], "]"]], RowBox[List["UnitStep", "[", "a", "]"]]]], "+", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "x"]], "-", FractionBox["b", "a"]]], "]"]], RowBox[List["UnitStep", "[", RowBox[List["-", "a"]], "]"]]]]]]]], "/;", " ", RowBox[List[RowBox[List["a", "\[Element]", "Reals"]], "\[And]", RowBox[List["b", "\[Element]", "Reals"]]]]]]]]
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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> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> x </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> b </mi> <mi> a </mi> </mfrac> </mrow> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mfrac> <mi> b </mi> <mi> a </mi> </mfrac> <mo> + </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> a </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> b </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> UnitStep </ci> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> x </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> <apply> <ci> UnitStep </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> UnitStep </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> x </ci> </apply> </apply> <apply> <ci> UnitStep </ci> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> a </ci> <reals /> </apply> <apply> <in /> <ci> b </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["a_", " ", "x_"]], "+", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["x", "+", FractionBox["b", "a"]]], "]"]], " ", RowBox[List["UnitStep", "[", "a", "]"]]]], "+", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "x"]], "-", FractionBox["b", "a"]]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List["-", "a"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["a", "\[Element]", "Reals"]], "&&", RowBox[List["b", "\[Element]", "Reals"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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