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 Cosh

 http://functions.wolfram.com/01.20.21.1423.01

 Input Form

 Integrate[z^n E^(b Sqrt[z] + e) Cos[a Sqrt[z] + q] Cosh[c Sqrt[z] + g], z] == (1/2) ((-((-I) a - b - c)^(-2 (1 + n))) E^(e + g + I q) Gamma[2 (1 + n), ((-I) a - b - c) Sqrt[z]] - (E^(e + g - I q) Gamma[2 (1 + n), (I a - b - c) Sqrt[z]])/ (I a - b - c)^(2 (1 + n)) - (E^(e - g + I q) Gamma[2 (1 + n), ((-I) a - b + c) Sqrt[z]])/ ((-I) a - b + c)^(2 (1 + n)) - (E^(e - g - I q) Gamma[2 (1 + n), (I a - b + c) Sqrt[z]])/ (I a - b + c)^(2 (1 + n))) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n z b + e cos ( z a + q ) cosh ( z c + g ) z 1 2 ( - ( - b - c - a ) - 2 ( n + 1 ) e + g + q Γ ( 2 ( n + 1 ) , ( - b - c - a ) z ) - ( - b - c + a ) - 2 ( n + 1 ) e + g - q Γ ( 2 ( n + 1 ) , ( - b - c + a ) z ) - ( - b + c - a ) - 2 ( n + 1 ) e - g + q Γ ( 2 ( n + 1 ) , ( - b + c - a ) z ) - ( - b + c + a ) - 2 ( n + 1 ) e - g - q Γ ( 2 ( n + 1 ) , ( - b + c + a ) z ) ) /; n Condition z z n z 1 2 b e z 1 2 a q z 1 2 c g 1 2 -1 -1 b -1 c -1 a -2 n 1 e g q Gamma 2 n 1 -1 b -1 c -1 a z 1 2 -1 -1 b -1 c a -2 n 1 e g -1 q Gamma 2 n 1 -1 b -1 c a z 1 2 -1 -1 b c -1 a -2 n 1 e -1 g q Gamma 2 n 1 -1 b c -1 a z 1 2 -1 -1 b c a -2 n 1 e -1 g -1 q Gamma 2 n 1 -1 b c a z 1 2 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", "e_"]]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", "q_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "b", "-", "c"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "b", "-", "c"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "b", "-", "c"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "b", "+", "c"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "-", "b", "+", "c"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "b", "+", "c"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g", "-", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", "b", "+", "c"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2002-12-18