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 Erfc

 http://functions.wolfram.com/06.27.21.0093.01

 Input Form

 Integrate[(Cosh[b z^2] Erfc[a z])/z, z] == (1/2) CoshIntegral[b z^2] + ((a z)/(2 Sqrt[Pi b z^2])) Sum[(a^(2 k)/((-b)^k ((1 + 2 k) k!))) Gamma[1/2 + k, b z^2], {k, 0, Infinity}] + ((a z)/(2 Sqrt[(-Pi) b z^2])) Sum[(a^(2 k)/(b^k ((1 + 2 k) k!))) Gamma[1/2 + k, (-b) z^2], {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], " ", RowBox[List["Erfc", "[", RowBox[List["a", " ", "z"]], "]"]]]], "z"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["a", " ", "z"]], RowBox[List["2", SqrtBox[RowBox[List["\[Pi]", " ", "b", " ", SuperscriptBox["z", "2"]]]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["-", "k"]]], SuperscriptBox["a", RowBox[List["2", "k"]]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], RowBox[List["k", "!"]]]]], RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "k"]], ",", RowBox[List["b", " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]], "+", RowBox[List[FractionBox[RowBox[List["a", " ", "z"]], RowBox[List["2", SqrtBox[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "b", " ", SuperscriptBox["z", "2"]]]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["b", RowBox[List["-", "k"]]], SuperscriptBox["a", RowBox[List["2", "k"]]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], RowBox[List["k", "!"]]]]], RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "k"]], ",", RowBox[List[RowBox[List["-", "b"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]]]]]]]]

 MathML Form

 cosh ( b z 2 ) erfc ( a z ) z z 1 2 Chi ( b z 2 ) + a z 2 π b z 2 k = 0 ( - b ) - k a 2 k Γ ( k + 1 2 , b z 2 ) ( 2 k + 1 ) k ! + a z 2 - π b z 2 k = 0 b - k a 2 k Γ ( k + 1 2 , - b z 2 ) ( 2 k + 1 ) k ! z b z 2 Erfc a z z -1 1 2 CoshIntegral b z 2 a z 2 b z 2 1 2 -1 k 0 -1 b -1 k a 2 k Gamma k 1 2 b z 2 2 k 1 k -1 a z 2 -1 b z 2 1 2 -1 k 0 b -1 k a 2 k Gamma k 1 2 -1 b z 2 2 k 1 k -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "]"]], " ", RowBox[List["Erfc", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["-", "k"]]], " ", SuperscriptBox["a", RowBox[List["2", " ", "k"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "k"]], ",", RowBox[List["b", " ", SuperscriptBox["z", "2"]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], " ", RowBox[List["k", "!"]]]]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[Pi]", " ", "b", " ", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", RowBox[List["-", "k"]]], " ", SuperscriptBox["a", RowBox[List["2", " ", "k"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "k"]], ",", RowBox[List[RowBox[List["-", "b"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], " ", RowBox[List["k", "!"]]]]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "b", " ", SuperscriptBox["z", "2"]]]]]]]]]]]]]

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

 2001-10-29