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 Cosh

 http://functions.wolfram.com/01.20.21.1356.01

 Input Form

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

 Standard Form

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 MathML Form

 z n p z 2 sin ( b z ) cosh ( c z ) z 1 8 p ( b 2 - c 2 2 p ( ( c - b ) 2 4 p q = 0 n 2 q - n ( - c - b ) n - q p - n - 1 2 ( c + b + 2 p z ) q + 1 ( - ( c + b + 2 p z ) 2 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 , - ( c + b + 2 p z ) 2 4 p ) - ( c + b ) 2 4 p q = 0 n 2 q - n ( b - c ) n - q p - n - 1 2 ( c - b + 2 p z ) q + 1 ( - ( c - b + 2 p z ) 2 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 , - ( c - b + 2 p z ) 2 4 p ) - ( c - b ) 2 4 p q = 0 n 2 q - n ( c + b ) n - q p - n - 1 2 ( - ( c + b - 2 p z ) 2 p ) 1 2 ( - q - 1 ) ( - c - b + 2 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 , - ( c + b - 2 p z ) 2 4 p ) + ( c + b ) 2 4 p q = 0 n 2 q - n ( c - b ) n - q p - n - 1 2 ( - ( c - b - 2 p z ) 2 p ) 1 2 ( - q - 1 ) ( - c + b + 2 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 , - ( c - b - 2 p z ) 2 4 p ) ) ) /; n Condition z z n p z 2 b z c z 1 8 p 1 2 -1 b 2 -1 c 2 2 p -1 c -1 b 2 4 p -1 q 0 n 2 q -1 n -1 c -1 b n -1 q p -1 n -1 1 2 c b 2 p z q 1 -1 c b 2 p z 2 p -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c b 2 p z 2 4 p -1 -1 c b 2 4 p -1 q 0 n 2 q -1 n b -1 c n -1 q p -1 n -1 1 2 c -1 b 2 p z q 1 -1 c -1 b 2 p z 2 p -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c -1 b 2 p z 2 4 p -1 -1 c -1 b 2 4 p -1 q 0 n 2 q -1 n c b n -1 q p -1 n -1 1 2 -1 c b -1 2 p z 2 p -1 1 2 -1 q -1 -1 c -1 b 2 p z q 1 Binomial n q Gamma q 1 2 -1 -1 c b -1 2 p z 2 4 p -1 c b 2 4 p -1 q 0 n 2 q -1 n c -1 b n -1 q p -1 n -1 1 2 -1 c -1 b -1 2 p z 2 p -1 1 2 -1 q -1 -1 c b 2 p z q 1 Binomial n q Gamma q 1 2 -1 -1 c -1 b -1 2 p z 2 4 p -1 n [/itex]

 Rule Form

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

 2002-12-18