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/01.20.21.1355.01

 Input Form

 Integrate[z^n E^(p Sqrt[z]) Sin[b Sqrt[z]] Cosh[c z], z] == (I 2^(-3 - 2 n) (E^((2 b^2 + 6 I b p + p^2)/(4 c)) Sum[(-(-1)^(-q + r)) 4^r ((-I) b + p)^(2 n - q - r) ((b + I (p + 2 c Sqrt[z]))^2/c)^((1/2) (-1 - q - r)) ((-I) b + p + 2 c Sqrt[z])^(q + r) Binomial[n, r] Binomial[r, q] ((b + I p) (b + I (p + 2 c Sqrt[z])) Gamma[(1/2) (1 + q + r), (b + I (p + 2 c Sqrt[z]))^2/(4 c)] - 2 c Sqrt[(b + I (p + 2 c Sqrt[z]))^2/c] Gamma[(1/2) (2 + q + r), (b + I (p + 2 c Sqrt[z]))^2/(4 c)]), {r, 0, n}, {q, 0, r}] + E^((p (2 I b + 3 p))/(4 c)) Sum[(-(-1)^(-q + r)) 4^r ((-I) b + p)^(2 n - q - r) ((-I) b + p - 2 c Sqrt[z])^(q + r) (((-I) b + p - 2 c Sqrt[z])^2/c)^((1/2) (-1 - q - r)) Binomial[n, r] Binomial[r, q] ((b + I p) (b + I (p - 2 c Sqrt[z])) Gamma[(1/2) (1 + q + r), ((-I) b + p - 2 c Sqrt[z])^2/(4 c)] + 2 c Sqrt[((-I) b + p - 2 c Sqrt[z])^2/c] Gamma[(1/2) (2 + q + r), ((-I) b + p - 2 c Sqrt[z])^2/(4 c)]), {r, 0, n}, {q, 0, r}] - E^((3 p (2 I b + p))/(4 c)) Sum[(-1)^(-q + r) 4^r (I b + p)^(2 n - q - r) (I b + p - 2 c Sqrt[z])^(q + r) ((I b + p - 2 c Sqrt[z])^2/c)^((1/2) (-1 - q - r)) Binomial[n, r] Binomial[r, q] ((I b + p) (I b + p - 2 c Sqrt[z]) Gamma[(1/2) (1 + q + r), (I b + p - 2 c Sqrt[z])^2/(4 c)] - 2 c Sqrt[(I b + p - 2 c Sqrt[z])^2/c] Gamma[(1/2) (2 + q + r), (I b + p - 2 c Sqrt[z])^2/(4 c)]), {r, 0, n}, {q, 0, r}] - E^((2 b^2 + 2 I b p + p^2)/(4 c)) Sum[(-1)^(-q + r) 4^r (I b + p)^(2 n - q - r) (I b + p + 2 c Sqrt[z])^(q + r) (-((I b + p + 2 c Sqrt[z])^2/c))^((1/2) (-1 - q - r)) Binomial[n, r] Binomial[r, q] ((I b + p) (I b + p + 2 c Sqrt[z]) Gamma[(1/2) (1 + q + r), -((I b + p + 2 c Sqrt[z])^2/(4 c))] + 2 c Sqrt[-((I b + p + 2 c Sqrt[z])^2/c)] Gamma[(1/2) (2 + q + r), -((I b + p + 2 c Sqrt[z])^2/(4 c))]), {r, 0, n}, {q, 0, r}]))/ (c^(2 (1 + n)) E^((b^2 + 4 I b p + 2 p^2)/(4 c))) /; 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 c - 2 ( n + 1 ) - b 2 + 4 p b + 2 p 2 4 c ( 2 b 2 + 6 p b + p 2 4 c r = 0 n q = 0 r - ( - 1 ) r - q 4 r ( - b + p ) 2 n - q - r ( ( b + ( 2 z c + p ) ) 2 c ) 1 2 ( - q - r - 1 ) ( 2 z c - b + p ) 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 + p ) ( b + ( 2 z c + p ) ) Γ ( 1 2 ( q + r + 1 ) , ( b + ( 2 z c + p ) ) 2 4 c ) - 2 c ( b + ( 2 z c + p ) ) 2 c Γ ( 1 2 ( q + r + 2 ) , ( b + ( 2 z c + p ) ) 2 4 c ) ) + p ( 2 b + 3 p ) 4 c r = 0 n q = 0 r - ( - 1 ) r - q 4 r ( - b + p ) 2 n - q - r ( - 2 z c - b + p ) q + r ( ( - 2 z c - b + p ) 2 c ) 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 + p ) ( b + ( p - 2 c z ) ) Γ ( 1 2 ( q + r + 1 ) , ( - 2 z c - b + p ) 2 4 c ) + 2 ( - 2 z c - b + p ) 2 c c Γ ( 1 2 ( q + r + 2 ) , ( - 2 z c - b + p ) 2 4 c ) ) - 3 p ( 2 b + p ) 4 c r = 0 n q = 0 r ( - 1 ) r - q 4 r ( b + p ) 2 n - q - r ( - 2 z c + b + p ) q + r ( ( - 2 z c + b + p ) 2 c ) 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 + p ) ( - 2 z c + b + p ) Γ ( 1 2 ( q + r + 1 ) , ( - 2 z c + b + p ) 2 4 c ) - 2 c ( - 2 z c + b + p ) 2 c Γ ( 1 2 ( q + r + 2 ) , ( - 2 z c + b + p ) 2 4 c ) ) - 2 b 2 + 2 p b + p 2 4 c r = 0 n q = 0 r ( - 1 ) r - q 4 r ( b + p ) 2 n - q - r ( 2 z c + b + p ) q + r ( - ( 2 z c + b + p ) 2 c ) 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 + p ) ( 2 z c + b + p ) Γ ( 1 2 ( q + r + 1 ) , - ( 2 z c + b + p ) 2 4 c ) + 2 - ( 2 z c + b + p ) 2 c c Γ ( 1 2 ( q + r + 2 ) , - ( 2 z c + b + p ) 2 4 c ) ) ) /; n Condition z z n p z 1 2 b z 1 2 c z 2 -2 n -3 c -2 n 1 -1 b 2 4 p b 2 p 2 4 c -1 2 b 2 6 p b p 2 4 c -1 q 0 r r 0 n -1 -1 r -1 q 4 r -1 b p 2 n -1 q -1 r b 2 z 1 2 c p 2 c -1 1 2 -1 q -1 r -1 2 z 1 2 c -1 b p q r Binomial n r Binomial r q b p b 2 z 1 2 c p Gamma 1 2 q r 1 b 2 z 1 2 c p 2 4 c -1 -1 2 c b 2 z 1 2 c p 2 c -1 1 2 Gamma 1 2 q r 2 b 2 z 1 2 c p 2 4 c -1 p 2 b 3 p 4 c -1 q 0 r r 0 n -1 -1 r -1 q 4 r -1 b p 2 n -1 q -1 r -2 z 1 2 c -1 b p q r -2 z 1 2 c -1 b p 2 c -1 1 2 -1 q -1 r -1 Binomial n r Binomial r q b p b p -1 2 c z 1 2 Gamma 1 2 q r 1 -2 z 1 2 c -1 b p 2 4 c -1 2 -2 z 1 2 c -1 b p 2 c -1 1 2 c Gamma 1 2 q r 2 -2 z 1 2 c -1 b p 2 4 c -1 -1 3 p 2 b p 4 c -1 q 0 r r 0 n -1 r -1 q 4 r b p 2 n -1 q -1 r -2 z 1 2 c b p q r -2 z 1 2 c b p 2 c -1 1 2 -1 q -1 r -1 Binomial n r Binomial r q b p -2 z 1 2 c b p Gamma 1 2 q r 1 -2 z 1 2 c b p 2 4 c -1 -1 2 c -2 z 1 2 c b p 2 c -1 1 2 Gamma 1 2 q r 2 -2 z 1 2 c b p 2 4 c -1 -1 2 b 2 2 p b p 2 4 c -1 q 0 r r 0 n -1 r -1 q 4 r b p 2 n -1 q -1 r 2 z 1 2 c b p q r -1 2 z 1 2 c b p 2 c -1 1 2 -1 q -1 r -1 Binomial n r Binomial r q b p 2 z 1 2 c b p Gamma 1 2 q r 1 -1 2 z 1 2 c b p 2 4 c -1 2 -1 2 z 1 2 c b p 2 c -1 1 2 c Gamma 1 2 q r 2 -1 2 z 1 2 c b p 2 4 c -1 n [/itex]

 Rule Form

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

 2002-12-18