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/01.20.21.1386.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18