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/01.20.21.1438.01

 Input Form

 Integrate[z^n E^(p z) Cos[b z^2]^m Cosh[c z], z] == 2^(-2 - m) (2 z^(1 + n) Binomial[m, m/2] (ExpIntegralE[-n, (c - p) z] + ExpIntegralE[-n, (-(c + p)) z]) (-1 + Mod[m, 2]) + Sum[E^((I (c + p)^2)/(b (8 k - 4 m))) Binomial[m, k] (((-I) b E^((I c p)/(-2 b k + b m)) (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}] + I 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)] Sqrt[I b (-2 k + m)] (E^((I c p)/(2 b k - b m)) Sum[2^(-n + q) (I b (-2 k + m))^(-(1/2) - n) (c - p)^(n - q) ((I (c - p + 2 I b (2 k - m) z)^2)/(b (-2 k + m)))^((1/2) (-1 - q)) (-c + p - 4 I b k z + 2 I b m z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, (-c + p - 4 I b k z + 2 I b m z)^2/(8 I b k - 4 I b m)], {q, 0, n}] + 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, (c + p - 4 I b k z + 2 I b m z)^2/(8 I b k - 4 I b m)], {q, 0, n}]))/E^((I (c + p)^2)/(b (4 k - 2 m))))/ (I b (2 k - m))^(3/2)), {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 cos m ( b z 2 ) cosh ( c z ) z 2 - m - 2 ( 2 ( 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]]]]] ( E TagBox["E", ExpIntegralE] - n ( ( c - p ) z ) + E TagBox["E", ExpIntegralE] - n ( - ( c + p ) z ) ) ( m mod 2 \$CellContext`m 2 - 1 ) z n + 1 + k = 0 m - 1 2 1 ( b ( 2 k - m ) ) 3 / 2 ( c + p ) 2 b ( 8 k - 4 m ) ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - b c p b m - 2 b k ( 2 k - m ) 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 ( 2 k - m ) ) 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 ) ) + b ( m - 2 k ) 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 ( 2 k - m ) ) 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 ) ) + - ( c + p ) 2 b ( 4 k - 2 m ) b ( 2 k - m ) b ( m - 2 k ) ( c p 2 b k - b m q = 0 n 2 q - n ( b ( m - 2 k ) ) - n - 1 2 ( c - p ) n - q ( ( c - p + 2 b ( 2 k - m ) z ) 2 b ( m - 2 k ) ) 1 2 ( - q - 1 ) ( - c + p - 4 b k z + 2 b m z ) 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 - 4 b k z + 2 b m z ) 2 8 b k - 4 b m ) + 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 - 4 b k z + 2 b m z ) 2 8 b k - 4 b m ) ) ) ) /; m + n Condition z z n p z b z 2 m c z 2 -1 m -2 2 Binomial m m 2 -1 ExpIntegralE -1 n c -1 p z ExpIntegralE -1 n -1 c p z \$CellContext`m 2 -1 z n 1 k 0 m -1 2 -1 1 b 2 k -1 m 3 2 -1 c p 2 b 8 k -1 4 m -1 Binomial m k -1 b c p b m -1 2 b k -1 2 k -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 p 2 b 2 k -1 m z 2 b 2 k -1 m -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 c p 2 b 2 k -1 m z 2 b 8 k -1 4 m -1 b m -1 2 k 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 c p 2 b 2 k -1 m z 2 b 2 k -1 m -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 c p 2 b 4 k -1 2 m -1 b 2 k -1 m 1 2 b m -1 2 k 1 2 c p 2 b k -1 b m -1 q 0 n 2 q -1 n b m -1 2 k -1 n -1 1 2 c -1 p n -1 q c -1 p 2 b 2 k -1 m z 2 b m -1 2 k -1 1 2 -1 q -1 -1 c p -1 4 b k z 2 b m z q 1 Binomial n q Gamma q 1 2 -1 -1 c p -1 4 b k z 2 b m z 2 8 b k -1 4 b m -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 c p -1 4 b k z 2 b m z 2 8 b k -1 4 b m -1 m SuperPlus n [/itex]

 Rule Form

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

 2002-12-18