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 | | http://functions.wolfram.com/06.38.19.0001.01 | 
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 | | Re[CosIntegral[x + I y]] == (1/2) Log[x^2 + y^2] + 
  (1/2) Sum[(y^(2 k)/(k (2 k)!)) HypergeometricPFQ[{k}, {1/2, 1 + k}, 
      -(x^2/4)], {k, 1, Infinity}] + CosIntegral[x] - Log[x] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Re", "[", RowBox[List["CosIntegral", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["Log", "[", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[FractionBox[SuperscriptBox["y", RowBox[List["2", " ", "k"]]], RowBox[List["k", " ", RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "k", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["1", "+", "k"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], "4"]]]]], "]"]]]]]]]], "+", RowBox[List["CosIntegral", "[", "x", "]"]], "-", RowBox[List["Log", "[", "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>  <mi> Re </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> Ci </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> x </mi>  <mo> + </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> y </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mrow>  <mi> Ci </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> x </mi>  <mo> ) </mo>  </mrow>  <mo> - </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> x </mi>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msup>  <mi> x </mi>  <mn> 2 </mn>  </msup>  <mo> + </mo>  <msup>  <mi> y </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> ∞ </mi>  </munderover>  <mrow>  <mfrac>  <msup>  <mi> y </mi>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> k </mi>  </mrow>  </msup>  <mrow>  <mi> k </mi>  <mo> ⁢ </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> k </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ! </mo>  </mrow>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 1 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> ; </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mi> x </mi>  <mn> 2 </mn>  </msup>  <mn> 4 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox["k", HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["k", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], "4"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  </mrow>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <times />  <real />  <apply>  <ci> CosIntegral </ci>  <apply>  <plus />  <ci> x </ci>  <apply>  <times />  <imaginaryi />  <ci> y </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <ci> CosIntegral </ci>  <ci> x </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ln />  <ci> x </ci>  </apply>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <ln />  <apply>  <plus />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> y </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <sum />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <infinity />  </uplimit>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <ci> y </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> k </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <ci> k </ci>  <apply>  <factorial />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> k </ci>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <ci> k </ci>  </list>  <list>  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <plus />  <ci> k </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> x </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Re", "[", RowBox[List["CosIntegral", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["y", RowBox[List["2", " ", "k"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "k", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["1", "+", "k"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], "4"]]]]], "]"]]]], RowBox[List["k", " ", RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]]]]]]]]], "+", RowBox[List["CosIntegral", "[", "x", "]"]], "-", RowBox[List["Log", "[", "x", "]"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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