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/01.20.21.1436.01

 Input Form

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

 Rule Form

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

 2002-12-18