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/01.20.21.4451.01

 Input Form

 Integrate[z^n Sinh[b z^2] Cosh[c z]^v, z] == 2^(-2 - v) (z^(1 + n) ((-b^2) z^4)^((1/2) (-1 - n)) Binomial[v, v/2] ((b z^2)^((1 + n)/2) Gamma[(1 + n)/2, (-b) z^2] - ((-b) z^2)^((1 + n)/2) Gamma[(1 + n)/2, b z^2]) (-1 + Mod[v, 2]) + b^(-1 - n) Sum[E^((c^2 (-2 s + v)^2)/(4 b)) Binomial[v, s] ((-E^(-((c^2 (-2 s + v)^2)/(2 b)))) Sum[2^(-n + q) (c (-2 s + v))^(n - q) (-((-2 c s + c v - 2 b z)^2/b))^((1/2) (-1 - q)) (c (2 s - v) + 2 b z)^(1 + q) Binomial[n, q] Gamma[(1 + q)/2, -((-2 c s + c v - 2 b z)^2/(4 b))], {q, 0, n}] + (-1)^(1 + n) Sum[(c (s - v/2))^(n - q) (-2 c s + c v - 2 b z)^(1 + q) ((-2 c s + c v - 2 b z)^2/b)^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (-2 c s + c v - 2 b z)^2/(4 b)], {q, 0, n}] + Sum[(c (s - v/2))^(n - q) (2 c s - c v - 2 b z) (c (-2 s + v) + 2 b z)^q (-((c (-2 s + v) + 2 b z)^2/b))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((-2 c s + c v + 2 b z)^2/(4 b))], {q, 0, n}]/ E^((c^2 (-2 s + v)^2)/(2 b)) + (-1)^(1 + n) Sum[2^(-n + q) (c (-2 s + v))^(n - q) (2 c s - c v - 2 b z)^(1 + q) ((c (-2 s + v) + 2 b z)^2/b)^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (-2 c s + c v + 2 b z)^2/(4 b)], {q, 0, n}]), {s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18