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/01.20.21.3978.01

 Input Form

 Integrate[z^n E^(p z) Cos[b z] Cosh[c z^2]^v, z] == 2^(-2 - v) (2 z^(1 + n) Binomial[v, v/2] (ExpIntegralE[-n, ((-I) b - p) z] + ExpIntegralE[-n, (I b - p) z]) (-1 + Mod[v, 2]) + Sum[((1/(c (2 k - v))^(3/2)) Binomial[v, k] (c (-2 k + v) Sum[2^(-n + q) ((-I) b - p)^(n - q) (c (2 k - v))^ (-(1/2) - n) (I b + p + 4 c k z - 2 c v z)^(1 + q) (-((I b + p + 4 c k z - 2 c v z)^2/(c (2 k - v))))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I b + p + 4 c k z - 2 c v z)^2/(c (8 k - 4 v)))], {q, 0, n}] + Sqrt[c (2 k - v)] Sqrt[c (-2 k + v)] (E^((-b^2 + p^2)/(c (4 k - 2 v))) Sum[2^(-n + q) (I b - p)^(n - q) (c (-2 k + v))^(-(1/2) - n) ((-I) b + p + 2 c (-2 k + v) z)^ (1 + q) (((-I) b + p + 2 c (-2 k + v) z)^2/(c (2 k - v)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, ((-I) b + p + 2 c (-2 k + v) z)^2/(c (8 k - 4 v))], {q, 0, n}] + E^((I b + p)^2/(c (4 k - 2 v))) Sum[2^(-n + q) ((-I) b - p)^(n - q) (c (-2 k + v))^(-(1/2) - n) (I b + p + 2 c (-2 k + v) z)^(1 + q) (-((I b + p + 2 c (-2 k + v) z)^2/(c (-2 k + v))))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I b + p + 2 c (-2 k + v) z)^2/(c (8 k - 4 v))], {q, 0, n}]) - c E^((I b p)/(c (2 k - v))) (2 k - v) Sum[2^(-n + q) (I b - p)^(n - q) (c (2 k - v))^(-(1/2) - n) ((-I) b + p + 4 c k z - 2 c v z)^(1 + q) (-(((-I) b + p + 4 c k z - 2 c v z)^2/(2 c k - c v)))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (b + I (p + 4 c k z - 2 c v z))^2/(c (8 k - 4 v))], {q, 0, n}]))/ E^((I b + p)^2/(c (8 k - 4 v))), {k, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0 && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos ( b z ) cosh v ( c z 2 ) z 2 - v - 2 ( 2 ( 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 TagBox["E", ExpIntegralE] - n ( ( - b - p ) z ) + E TagBox["E", ExpIntegralE] - n ( ( b - p ) z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) z n + 1 + k = 0 v - 1 2 1 ( c ( 2 k - v ) ) 3 / 2 - ( b + p ) 2 c ( 8 k - 4 v ) ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( 2 k - v ) c ( v - 2 k ) ( p 2 - b 2 c ( 4 k - 2 v ) q = 0 n 2 q - n ( b - p ) n - q ( c ( v - 2 k ) ) - n - 1 2 ( - b + p + 2 c ( v - 2 k ) z ) q + 1 ( ( - b + p + 2 c ( v - 2 k ) z ) 2 c ( 2 k - v ) ) 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 + p + 2 c ( v - 2 k ) z ) 2 c ( 8 k - 4 v ) ) + ( b + p ) 2 c ( 4 k - 2 v ) q = 0 n 2 q - n ( - b - p ) n - q ( c ( v - 2 k ) ) - n - 1 2 ( b + p + 2 c ( v - 2 k ) z ) q + 1 ( - ( b + p + 2 c ( v - 2 k ) z ) 2 c ( v - 2 k ) ) 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 + p + 2 c ( v - 2 k ) z ) 2 c ( 8 k - 4 v ) ) ) - c b p c ( 2 k - v ) ( 2 k - v ) q = 0 n 2 q - n ( b - p ) n - q ( c ( 2 k - v ) ) - n - 1 2 ( - b + p + 4 c k z - 2 c v z ) q + 1 ( - ( - b + p + 4 c k z - 2 c v z ) 2 2 c k - c v ) 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 + ( p + 4 c k z - 2 c v z ) ) 2 c ( 8 k - 4 v ) ) + c ( v - 2 k ) q = 0 n 2 q - n ( - b - p ) n - q ( c ( 2 k - v ) ) - n - 1 2 ( b + p + 4 c k z - 2 c v z ) q + 1 ( - ( b + p + 4 c k z - 2 c v z ) 2 c ( 2 k - v ) ) 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 + p + 4 c k z - 2 c v z ) 2 c ( 8 k - 4 v ) ) ) ) /; v + n Condition z z n p z b z c z 2 v 2 -1 v -2 2 Binomial v v 2 -1 ExpIntegralE -1 n -1 b -1 p z ExpIntegralE -1 n b -1 p z \$CellContext`v 2 -1 z n 1 k 0 v -1 2 -1 1 c 2 k -1 v 3 2 -1 -1 b p 2 c 8 k -1 4 v -1 Binomial v k c 2 k -1 v 1 2 c v -1 2 k 1 2 p 2 -1 b 2 c 4 k -1 2 v -1 q 0 n 2 q -1 n b -1 p n -1 q c v -1 2 k -1 n -1 1 2 -1 b p 2 c v -1 2 k z q 1 -1 b p 2 c v -1 2 k z 2 c 2 k -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 b p 2 c v -1 2 k z 2 c 8 k -1 4 v -1 b p 2 c 4 k -1 2 v -1 q 0 n 2 q -1 n -1 b -1 p n -1 q c v -1 2 k -1 n -1 1 2 b p 2 c v -1 2 k z q 1 -1 b p 2 c v -1 2 k z 2 c v -1 2 k -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b p 2 c v -1 2 k z 2 c 8 k -1 4 v -1 -1 c b p c 2 k -1 v -1 2 k -1 v q 0 n 2 q -1 n b -1 p n -1 q c 2 k -1 v -1 n -1 1 2 -1 b p 4 c k z -1 2 c v z q 1 -1 -1 b p 4 c k z -1 2 c v z 2 2 c k -1 c v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b p 4 c k z -1 2 c v z 2 c 8 k -1 4 v -1 c v -1 2 k q 0 n 2 q -1 n -1 b -1 p n -1 q c 2 k -1 v -1 n -1 1 2 b p 4 c k z -1 2 c v z q 1 -1 b p 4 c k z -1 2 c v z 2 c 2 k -1 v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 b p 4 c k z -1 2 c v z 2 c 8 k -1 4 v -1 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18