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/01.20.21.1359.01

 Input Form

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

 Standard Form

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 MathML Form

 z n p z sin ( b z ) cosh ( c z ) z - 2 - 2 n - 3 ( - b 2 4 p - 4 c ( r = 0 n q = 0 r - ( - 1 ) r - q 4 r ( - b ) 2 n - q - r ( ( b + 2 ( c - p ) z ) 2 c - p ) 1 2 ( - q - r - 1 ) ( - b + 2 ( p - c ) z ) q + r ( n r ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["r", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( r q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["r", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( b ( b - 2 ( c - p ) z ) Γ ( 1 2 ( q + r + 1 ) , ( b + 2 ( c - p ) z ) 2 4 ( c - p ) ) + 2 ( b + 2 ( c - p ) z ) 2 c - p ( c - p ) Γ ( 1 2 ( q + r + 2 ) , ( b + 2 ( c - p ) z ) 2 4 ( c - p ) ) ) ) ( p - c ) - 2 ( n + 1 ) + b 2 4 p - 4 c ( r = 0 n q = 0 r - ( - 1 ) r - q 4 r ( b ) 2 n - q - r ( b + 2 ( p - c ) z ) q + r ( ( b + 2 ( p - c ) z ) 2 c - p ) 1 2 ( - q - r - 1 ) ( n r ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["r", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( r q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["r", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( b ( b + 2 ( c - p ) z ) Γ ( 1 2 ( q + r + 1 ) , ( b + 2 ( p - c ) z ) 2 4 ( c - p ) ) + 2 ( b + 2 ( p - c ) z ) 2 c - p ( c - p ) Γ ( 1 2 ( q + r + 2 ) , ( b + 2 ( p - c ) z ) 2 4 ( c - p ) ) ) ) ( p - c ) - 2 ( n + 1 ) + b 2 4 ( c + p ) ( c + p ) - 2 ( n + 1 ) ( r = 0 n q = 0 r - ( - 1 ) r - q 4 r ( b ) 2 n - q - r ( ( b - 2 ( c + p ) z ) 2 c + p ) 1 2 ( - q - r - 1 ) ( b + 2 ( c + p ) z ) q + r ( n r ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["r", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( r q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["r", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( b ( b - 2 ( c + p ) z ) Γ ( 1 2 ( q + r + 1 ) , ( b - 2 ( c + p ) z ) 2 4 ( c + p ) ) - 2 ( c + p ) ( b - 2 ( c + p ) z ) 2 c + p Γ ( 1 2 ( q + r + 2 ) , ( b - 2 ( c + p ) z ) 2 4 ( c + p ) ) ) - r = 0 n q = 0 r - ( - 1 ) r - q 4 r ( - b ) 2 n - q - r ( ( b + 2 ( c + p ) z ) 2 c + p ) 1 2 ( - q - r - 1 ) ( - b + 2 ( c + p ) z ) q + r ( n r ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["r", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( r q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["r", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( b ( b + 2 ( c + p ) z ) Γ ( 1 2 ( q + r + 1 ) , ( b + 2 ( c + p ) z ) 2 4 ( c + p ) ) - 2 ( c + p ) ( b + 2 ( c + p ) z ) 2 c + p Γ ( 1 2 ( q + r + 2 ) , ( b + 2 ( c + p ) z ) 2 4 ( c + p ) ) ) ) ) /; n Condition z z n p z b z 1 2 c z -1 2 -2 n -3 -1 b 2 4 p -1 4 c -1 q 0 r r 0 n -1 -1 r -1 q 4 r -1 b 2 n -1 q -1 r b 2 c -1 p z 1 2 2 c -1 p -1 1 2 -1 q -1 r -1 -1 b 2 p -1 c z 1 2 q r Binomial n r Binomial r q b b -1 2 c -1 p z 1 2 Gamma 1 2 q r 1 b 2 c -1 p z 1 2 2 4 c -1 p -1 2 b 2 c -1 p z 1 2 2 c -1 p -1 1 2 c -1 p Gamma 1 2 q r 2 b 2 c -1 p z 1 2 2 4 c -1 p -1 p -1 c -2 n 1 b 2 4 p -1 4 c -1 q 0 r r 0 n -1 -1 r -1 q 4 r b 2 n -1 q -1 r b 2 p -1 c z 1 2 q r b 2 p -1 c z 1 2 2 c -1 p -1 1 2 -1 q -1 r -1 Binomial n r Binomial r q b b 2 c -1 p z 1 2 Gamma 1 2 q r 1 b 2 p -1 c z 1 2 2 4 c -1 p -1 2 b 2 p -1 c z 1 2 2 c -1 p -1 1 2 c -1 p Gamma 1 2 q r 2 b 2 p -1 c z 1 2 2 4 c -1 p -1 p -1 c -2 n 1 b 2 4 c p -1 c p -2 n 1 q 0 r r 0 n -1 -1 r -1 q 4 r b 2 n -1 q -1 r b -1 2 c p z 1 2 2 c p -1 1 2 -1 q -1 r -1 b 2 c p z 1 2 q r Binomial n r Binomial r q b b -1 2 c p z 1 2 Gamma 1 2 q r 1 b -1 2 c p z 1 2 2 4 c p -1 -1 2 c p b -1 2 c p z 1 2 2 c p -1 1 2 Gamma 1 2 q r 2 b -1 2 c p z 1 2 2 4 c p -1 -1 q 0 r r 0 n -1 -1 r -1 q 4 r -1 b 2 n -1 q -1 r b 2 c p z 1 2 2 c p -1 1 2 -1 q -1 r -1 -1 b 2 c p z 1 2 q r Binomial n r Binomial r q b b 2 c p z 1 2 Gamma 1 2 q r 1 b 2 c p z 1 2 2 4 c p -1 -1 2 c p b 2 c p z 1 2 2 c p -1 1 2 Gamma 1 2 q r 2 b 2 c p z 1 2 2 4 c p -1 n [/itex]

 Rule Form

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

 2002-12-18