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/01.20.21.4814.01

 Input Form

 Integrate[z^n E^(p z) Sinh[b z] Cosh[c z^2]^v, z] == 2^(-2 - v) (2 z^(1 + n) Binomial[v, v/2] (-ExpIntegralE[-n, (b - p) z] + ExpIntegralE[-n, (-(b + p)) z]) (-1 + Mod[v, 2]) - Sum[Binomial[v, s] ((1/Sqrt[c (2 s - v)]) (E^((b + p)^2/(4 c (-2 s + v))) Sum[(-(b/2) - p/2)^(n - q) (c (2 s - v))^(-(1/2) - n) (b + p + 4 c s z - 2 c v z)^(1 + q) (-((b + p + 4 c s z - 2 c v z)^2/(2 c s - c v)))^(-(1/2) - q/2) Binomial[n, q] Gamma[(1 + q)/2, -((b + p + 4 c s z - 2 c v z)^2/ (4 (2 c s - c v)))], {q, 0, n}]) - (1/Sqrt[c (2 s - v)]) (E^((b - p)^2/(4 c (-2 s + v))) Sum[2^(-n + q) (b - p)^(n - q) (c (2 s - v))^(-(1/2) - n) (-b + p + 4 c s z - 2 c v z)^(1 + q) (-((-b + p + 4 c s z - 2 c v z)^2/(2 c s - c v)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((b - p + 2 c (-2 s + v) z)^2/ (c (8 s - 4 v)))], {q, 0, n}]) - (1/Sqrt[c (-2 s + v)]) (E^((b - p)^2/(c (8 s - 4 v))) Sum[2^(-n + q) (b - p)^(n - q) (c (-2 s + v))^(-(1/2) - n) (-b + p + 2 c (-2 s + v) z)^(1 + q) (-((-b + p + 2 c (-2 s + v) z)^2/(c (-2 s + v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (-b + p + 2 c (-2 s + v) z)^2/ (c (8 s - 4 v))], {q, 0, n}]) + (1/Sqrt[c (-2 s + v)]) (E^((b + p)^2/(c (8 s - 4 v))) Sum[(-(b/2) - p/2)^(n - q) (c (-2 s + v))^(-(1/2) - n) (b + p + 2 c (-2 s + v) z)^(1 + q) (-((b + p + 2 c (-2 s + v) z)^2/(c (-2 s + v))))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (b + p + 2 c (-2 s + v) z)^2/ (c (8 s - 4 v))], {q, 0, n}])), {s, 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 sinh ( b z ) cosh v ( c z 2 ) z 2 - v - 2 ( 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 TagBox["E", ExpIntegralE] - n ( - ( b + p ) z ) - E TagBox["E", ExpIntegralE] - n ( ( b - p ) z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) - 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]]]]] ( - 1 c ( v - 2 s ) ( ( b - p ) 2 c ( 8 s - 4 v ) q = 0 n 2 q - n ( b - p ) n - q ( c ( v - 2 s ) ) - n - 1 2 ( - b + p + 2 c ( v - 2 s ) z ) q + 1 ( - ( - b + p + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) 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 s ) z ) 2 c ( 8 s - 4 v ) ) ) + 1 c ( v - 2 s ) ( ( b + p ) 2 c ( 8 s - 4 v ) q = 0 n ( - b 2 - p 2 ) n - q ( c ( v - 2 s ) ) - n - 1 2 ( b + p + 2 c ( v - 2 s ) z ) q + 1 ( - ( b + p + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) 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 s ) z ) 2 c ( 8 s - 4 v ) ) ) - 1 c ( 2 s - v ) ( ( b - p ) 2 4 c ( v - 2 s ) q = 0 n 2 q - n ( b - p ) n - q ( c ( 2 s - v ) ) - n - 1 2 ( - b + p + 4 c s z - 2 c v z ) q + 1 ( - ( - b + p + 4 c s z - 2 c v z ) 2 2 c s - 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 + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) ) + 1 c ( 2 s - v ) ( ( b + p ) 2 4 c ( v - 2 s ) q = 0 n ( - b 2 - p 2 ) n - q ( c ( 2 s - v ) ) - n - 1 2 ( b + p + 4 c s z - 2 c v z ) q + 1 ( - ( b + p + 4 c s z - 2 c v z ) 2 2 c s - c v ) - q 2 - 1 2 ( 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 s z - 2 c v z ) 2 4 ( 2 c s - c v ) ) ) ) ) /; v + n Condition z z n p z b z c z 2 v 2 -1 v -2 2 z n 1 Binomial v v 2 -1 ExpIntegralE -1 n -1 b p z -1 ExpIntegralE -1 n b -1 p z \$CellContext`v 2 -1 -1 s 0 v -1 2 -1 Binomial v s -1 1 c v -1 2 s 1 2 -1 b -1 p 2 c 8 s -1 4 v -1 q 0 n 2 q -1 n b -1 p n -1 q c v -1 2 s -1 n -1 1 2 -1 b p 2 c v -1 2 s z q 1 -1 -1 b p 2 c v -1 2 s z 2 c v -1 2 s -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 b p 2 c v -1 2 s z 2 c 8 s -1 4 v -1 1 c v -1 2 s 1 2 -1 b p 2 c 8 s -1 4 v -1 q 0 n -1 b 2 -1 -1 p 2 -1 n -1 q c v -1 2 s -1 n -1 1 2 b p 2 c v -1 2 s z q 1 -1 b p 2 c v -1 2 s z 2 c v -1 2 s -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b p 2 c v -1 2 s z 2 c 8 s -1 4 v -1 -1 1 c 2 s -1 v 1 2 -1 b -1 p 2 4 c v -1 2 s -1 q 0 n 2 q -1 n b -1 p n -1 q c 2 s -1 v -1 n -1 1 2 -1 b p 4 c s z -1 2 c v z q 1 -1 -1 b p 4 c s z -1 2 c v z 2 2 c s -1 c v -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 b -1 p 2 c v -1 2 s z 2 c 8 s -1 4 v -1 1 c 2 s -1 v 1 2 -1 b p 2 4 c v -1 2 s -1 q 0 n -1 b 2 -1 -1 p 2 -1 n -1 q c 2 s -1 v -1 n -1 1 2 b p 4 c s z -1 2 c v z q 1 -1 b p 4 c s z -1 2 c v z 2 2 c s -1 c v -1 -1 q 2 -1 -1 1 2 Binomial n q Gamma q 1 2 -1 -1 b p 4 c s z -1 2 c v z 2 4 2 c s -1 c v -1 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18