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http://functions.wolfram.com/03.13.07.0002.01
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KelvinBei[z] == (2/Pi) Integrate[(Sin[(t z)/Sqrt[2]] Sinh[(t z)/Sqrt[2]])/
Sqrt[1 - t^2], {t, 0, 1}]
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Cell[BoxData[RowBox[List[RowBox[List["KelvinBei", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["2", "\[Pi]"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["t", " ", "z"]], SqrtBox["2"]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["t", " ", "z"]], SqrtBox["2"]], "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["t", "2"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]
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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> <mi> bei </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mtext> </mtext> </mrow> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mfrac> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> t </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> t </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> t </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> KelvinBei </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <cn type='integer'> 1 </cn> </uplimit> <apply> <times /> <apply> <sin /> <apply> <times /> <ci> t </ci> <ci> z </ci> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> t </ci> <ci> z </ci> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> t </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBei", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List["t", " ", "z"]], SqrtBox["2"]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["t", " ", "z"]], SqrtBox["2"]], "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["t", "2"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "\[Pi]"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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