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 Cosh

 http://functions.wolfram.com/01.20.21.1362.01

 Input Form

 Integrate[z^n E^(p z^2) Sin[b z] Cosh[c z^2], z] == I E^(b^2/(-4 c + 4 p)) (((-Sqrt[c + p]) Sum[2^(-n + q) (I b)^(n - q) (-c + p)^(-(1/2) - n) ((I b + 2 (c - p) z)^2/(c - p))^((1/2) (-1 - q)) ((-I) b + 2 (-c + p) z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, (I b + 2 (c - p) z)^2/(4 (c - p))], {q, 0, n}] + Sqrt[c + p] Sum[2^(-n + q) ((-I) b)^(n - q) (-c + p)^(-(1/2) - n) (I b - 2 c z + 2 p z)^(1 + q) ((I b - 2 c z + 2 p z)^2/(c - p))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I b - 2 c z + 2 p z)^2/(4 (c - p))], {q, 0, n}] + E^((c b^2)/(2 c^2 - 2 p^2)) Sqrt[-c + p] (Sum[2^(-n + q) ((-I) b)^(n - q) (c + p)^(-(1/2) - n) ((b - 2 I (c + p) z)^2/(c + p))^((1/2) (-1 - q)) (I b + 2 (c + p) z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, (b - 2 I (c + p) z)^2/(4 (c + p))], {q, 0, n}] - Sum[2^(-n + q) (I b)^(n - q) (c + p)^(-(1/2) - n) ((b + 2 I (c + p) z)^2/(c + p))^((1/2) (-1 - q)) ((-I) b + 2 (c + p) z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, (b + 2 I (c + p) z)^2/(4 (c + p))], {q, 0, n}]))/ (8 Sqrt[-c + p] Sqrt[c + p])) /; Element[n, Integers] && n >= 0

 Standard Form

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RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]]], "]"]]]]]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["8", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", "p"]]], " ", SqrtBox[RowBox[List["c", "+", "p"]]]]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n p z 2 sin ( b z ) cosh ( c z 2 ) z 8 p - c c + p b 2 4 p - 4 c ( - c + p q = 0 n 2 q - n ( b ) n - q ( p - c ) - n - 1 2 ( ( b + 2 ( c - p ) z ) 2 c - p ) 1 2 ( - q - 1 ) ( - b + 2 ( p - c ) z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b + 2 ( c - p ) z ) 2 4 ( c - p ) ) + c + p q = 0 n 2 q - n ( - b ) n - q ( p - c ) - n - 1 2 ( b - 2 c z + 2 p z ) q + 1 ( ( b - 2 c z + 2 p z ) 2 c - p ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b - 2 c z + 2 p z ) 2 4 ( c - p ) ) + c b 2 2 c 2 - 2 p 2 p - c ( q = 0 n 2 q - n ( - b ) n - q ( c + p ) - n - 1 2 ( ( b - 2 ( c + p ) z ) 2 c + p ) 1 2 ( - q - 1 ) ( b + 2 ( c + p ) z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b - 2 ( c + p ) z ) 2 4 ( c + p ) ) - q = 0 n 2 q - n ( b ) n - q ( c + p ) - n - 1 2 ( ( b + 2 ( c + p ) z ) 2 c + p ) 1 2 ( - q - 1 ) ( - b + 2 ( c + p ) z ) q + 1 ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b + 2 ( c + p ) z ) 2 4 ( c + p ) ) ) ) /; n Condition z z n p z 2 b z c z 2 8 p -1 c 1 2 c p 1 2 -1 b 2 4 p -1 4 c -1 -1 c p 1 2 q 0 n 2 q -1 n b n -1 q p -1 c -1 n -1 1 2 b 2 c -1 p z 2 c -1 p -1 1 2 -1 q -1 -1 b 2 p -1 c z q 1 Binomial n q Gamma q 1 2 -1 b 2 c -1 p z 2 4 c -1 p -1 c p 1 2 q 0 n 2 q -1 n -1 b n -1 q p -1 c -1 n -1 1 2 b -1 2 c z 2 p z q 1 b -1 2 c z 2 p z 2 c -1 p -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b -1 2 c z 2 p z 2 4 c -1 p -1 c b 2 2 c 2 -1 2 p 2 -1 p -1 c 1 2 q 0 n 2 q -1 n -1 b n -1 q c p -1 n -1 1 2 b -1 2 c p z 2 c p -1 1 2 -1 q -1 b 2 c p z q 1 Binomial n q Gamma q 1 2 -1 b -1 2 c p z 2 4 c p -1 -1 q 0 n 2 q -1 n b n -1 q c p -1 n -1 1 2 b 2 c p z 2 c p -1 1 2 -1 q -1 -1 b 2 c p z q 1 Binomial n q Gamma q 1 2 -1 b 2 c p z 2 4 c p -1 n [/itex]

 Rule Form

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

 2002-12-18