html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.1354.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18