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 SinhIntegral

 http://functions.wolfram.com/06.39.06.0009.01

 Input Form

 SinhIntegral[z] == Pi Sum[(-1)^k BesselI[k + 1/2, z/2]^2, {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["SinhIntegral", "[", "z", "]"]], "\[Equal]", RowBox[List["\[Pi]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List[RowBox[List["k", "+", FractionBox["1", "2"]]], ",", FractionBox["z", "2"]]], "]"]], "2"]]]]]]]]]]]

 MathML Form

 Shi ( z ) π k = 0 ( - 1 ) k I k + 1 2 ( z 2 ) 2 SinhIntegral z k 0 -1 k BesselI k 1 2 z 2 -1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SinhIntegral", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[Pi]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox[RowBox[List["BesselI", "[", RowBox[List[RowBox[List["k", "+", FractionBox["1", "2"]]], ",", FractionBox["z", "2"]]], "]"]], "2"]]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29