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http://functions.wolfram.com/02.07.22.0003.01
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FourierCosTransform[Catalan, t, z] == Catalan Sqrt[Pi/2] DiracDelta[z]
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Cell[BoxData[RowBox[List[RowBox[List["FourierCosTransform", "[", RowBox[List["Catalan", ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Catalan", " ", SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", "z", "]"]]]]]]]]
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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> <mi> ℱ𝒸 </mi> <mi> t </mi> </msub> <mo> [ </mo> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox["C", Function[Catalan]] </annotation> </semantics> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox["C", Function[Catalan]] </annotation> </semantics> <mo> ⁢ </mo> <msqrt> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <mrow> <mi> δ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> ℱ𝒸 </ci> <ci> t </ci> </apply> <ci> Catalan </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <ci> Catalan </ci> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> δ </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierCosTransform", "[", RowBox[List["Catalan", ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Catalan", " ", SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["DiracDelta", "[", "z", "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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