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http://functions.wolfram.com/12.01.22.0006.01
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FourierTransform[1/Sqrt[Abs[t]], t, x] == 1/Sqrt[Abs[x]]
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Cell[BoxData[RowBox[List[RowBox[List["FourierTransform", "[", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["Abs", "[", "t", "]"]]]], ",", "t", ",", "x"]], "]"]], "\[Equal]", FractionBox["1", SqrtBox[RowBox[List["Abs", "[", "x", "]"]]]]]]]]
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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> ℱ </mi> <mi> t </mi> </msub> <mo> [ </mo> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> t </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </msqrt> </mfrac> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo>  </mo> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> x </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> FourierTransform </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <abs /> <ci> t </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> t </ci> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <abs /> <ci> x </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierTransform", "[", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["Abs", "[", "t_", "]"]]]], ",", "t_", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", SqrtBox[RowBox[List["Abs", "[", "x", "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
