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 Cosh

 http://functions.wolfram.com/01.20.21.4475.01

 Input Form

 Integrate[z^n Sinh[b z^2 + e] Cosh[c z^2]^v, z] == 2^(-2 - v) z^(1 + n) (Binomial[v, v/2] (E^e ((-b) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-b) z^2] - ((b z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, b z^2])/E^e) (-1 + Mod[v, 2]) - Sum[Binomial[v, s] (E^(2 e) ((-b + 2 c s - c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-b + 2 c s - c v) z^2] - ((b + 2 c s - c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (b + 2 c s - c v) z^2] + E^(2 e) ((-b - 2 c s + c v) z^2)^ ((1/2) (-1 - n)) Gamma[(1 + n)/2, (-b - 2 c s + c v) z^2] - ((b - 2 c s + c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (b - 2 c s + c v) z^2]), {s, 0, Floor[(1/2) (-1 + v)]}]/E^e) /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 z n sinh ( b z 2 + e ) cosh v ( c z 2 ) z 2 - v - 2 z n + 1 ( ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( e ( - b z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , - b z 2 ) - - e ( b z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , b z 2 ) ) ( v mod 2 \$CellContext`v 2 - 1 ) - - e s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 e Γ ( n + 1 2 , ( - b - 2 c s + c v ) z 2 ) ( ( - b - 2 c s + c v ) z 2 ) 1 2 ( - n - 1 ) - ( ( b - 2 c s + c v ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( b - 2 c s + c v ) z 2 ) + 2 e ( ( - b + 2 c s - c v ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + 2 c s - c v ) z 2 ) - ( ( b + 2 c s - c v ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( b + 2 c s - c v ) z 2 ) ) ) /; n v + Condition z z n b z 2 e c z 2 v 2 -1 v -2 z n 1 Binomial v v 2 -1 e -1 b z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b z 2 -1 -1 e b z 2 1 2 -1 n -1 Gamma n 1 2 -1 b z 2 \$CellContext`v 2 -1 -1 -1 e s 0 v -1 2 -1 Binomial v s 2 e Gamma n 1 2 -1 -1 b -1 2 c s c v z 2 -1 b -1 2 c s c v z 2 1 2 -1 n -1 -1 b -1 2 c s c v z 2 1 2 -1 n -1 Gamma n 1 2 -1 b -1 2 c s c v z 2 2 e -1 b 2 c s -1 c v z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b 2 c s -1 c v z 2 -1 b 2 c s -1 c v z 2 1 2 -1 n -1 Gamma n 1 2 -1 b 2 c s -1 c v z 2 n v SuperPlus [/itex]

 Rule Form

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

 2002-12-18