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http://functions.wolfram.com/06.37.26.0019.01
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CosIntegral[Sqrt[z]]^2 + SinIntegral[Sqrt[z]]^2 ==
Pi^2/4 + (Pi^(3/2)/2) MeijerG[{{0}, {1/2, 1}}, {{0, 0, 0}, {1/2, 1/2}}, z/4]
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Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["CosIntegral", "[", SqrtBox["z"], "]"]], "2"], "+", SuperscriptBox[RowBox[List["SinIntegral", "[", SqrtBox["z"], "]"]], "2"]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "+", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], "2"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", FractionBox["z", "4"]]], "]"]]]]]]]]]]
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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> <msup> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> π </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mi> z </mi> <mn> 4 </mn> </mfrac> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "5"]], RowBox[List["3", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox["z", "4"], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["1", MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> + </mo> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <power /> <apply> <ci> CosIntegral </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> SinIntegral </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <ci> MeijerG </ci> <list> <list> <cn type='integer'> 0 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 1 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["CosIntegral", "[", SqrtBox["z_"], "]"]], "2"], "+", SuperscriptBox[RowBox[List["SinIntegral", "[", SqrtBox["z_"], "]"]], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", "0"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", FractionBox["z", "4"]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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