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/01.20.21.1390.01

 Input Form

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

 Rule Form

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

 2002-12-18