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/01.20.21.1364.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18