Sine: Integral transforms (formula 01.06.22.0008)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Integral transforms

Hilbert transforms

http://functions.wolfram.com/01.06.22.0008.01

Input Form

HilbertTransform[Sin[t], t, x] == Cos[x]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HilbertTransform", "[", RowBox[List[RowBox[List["Sin", "[", "t", "]"]], ",", "t", ",", "x"]], "]"]], "\[Equal]", RowBox[List["Cos", "[", "x", "]"]]]]]]

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> <mi> ℋ </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> ℋ </ci> <ci> t </ci> </apply> <apply> <sin /> <ci> t </ci> </apply> </apply> <ci> x </ci> </apply> <apply> <cos /> <ci> x </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HilbertTransform", "[", RowBox[List[RowBox[List["Sin", "[", "t_", "]"]], ",", "t_", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Cos", "[", "x", "]"]]]]]]

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

2001-10-29