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/01.20.21.3916.01

 Input Form

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

 Standard Form

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"2"]]], "b"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "q"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "q"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "q"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]], "]"]]]]]]]], ")"]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n p z sin ( b z 2 ) cosh v ( c z ) z - 2 - v - 2 ( b ) - n - 1 ( p 2 4 b ( 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]]]]] ( v mod 2 \$CellContext`v 2 - 1 ) ( q = 0 n 2 q - n ( - p ) n - q ( p + 2 b z ) q + 1 ( ( p + 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 , ( p + 2 b z ) 2 4 b ) + ( - 1 ) n - p 2 2 b q = 0 n 2 q - n ( - p ) n - q ( p - 2 b z ) q + 1 ( - ( p - 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 , - ( p - 2 b z ) 2 4 b ) ) - s = 0 v - 1 2 ( p + c ( 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]]]]] ( q = 0 n 2 q - n ( - p + 2 c s - c v ) n - q ( p - 2 c s + c v + 2 b z ) q + 1 ( ( p - 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 , ( p - 2 c s + c v + 2 b z ) 2 4 b ) + - c p ( v - 2 s ) b q = 0 n 2 q - n ( - p - 2 c s + c v ) n - q ( p + 2 c s - c v + 2 b z ) q + 1 ( ( p + 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 , ( p + 2 c s - c v + 2 b z ) 2 4 b ) + ( - 1 ) n - ( p + c ( v - 2 s ) ) 2 2 b q = 0 n 2 q - n ( - p + 2 c s - c v ) n - q ( p - 2 c s + c v - 2 b z ) q + 1 ( - ( p - 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 , - ( p - 2 c s + c v - 2 b z ) 2 4 b ) + ( - 1 ) n - ( p 2 + c 2 ( v - 2 s ) 2 ) 2 b q = 0 n 2 q - n ( c ( v - 2 s ) - p ) n - q ( p + 2 c s - c v - 2 b z ) q + 1 ( - ( p + 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 , - ( p + 2 c s - c v - 2 b z ) 2 4 b ) ) ) /; v + n Condition z z n p z b z 2 c z v -1 2 -1 v -2 b -1 n -1 p 2 4 b -1 Binomial v v 2 -1 \$CellContext`v 2 -1 q 0 n 2 q -1 n -1 p n -1 q p 2 b z q 1 p 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 p 2 b z 2 4 b -1 -1 n -1 p 2 2 b -1 q 0 n 2 q -1 n -1 p n -1 q p -1 2 b z q 1 -1 p -1 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 p -1 2 b z 2 4 b -1 -1 s 0 v -1 2 -1 p c v -1 2 s 2 4 b -1 Binomial v s q 0 n 2 q -1 n -1 p 2 c s -1 c v n -1 q p -1 2 c s c v 2 b z q 1 p -1 2 c s c v 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 p -1 2 c s c v 2 b z 2 4 b -1 -1 c p v -1 2 s b -1 q 0 n 2 q -1 n -1 p -1 2 c s c v n -1 q p 2 c s -1 c v 2 b z q 1 p 2 c s -1 c v 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 p 2 c s -1 c v 2 b z 2 4 b -1 -1 n -1 p c v -1 2 s 2 2 b -1 q 0 n 2 q -1 n -1 p 2 c s -1 c v n -1 q p -1 2 c s c v -1 2 b z q 1 -1 p -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 -1 p -1 2 c s c v -1 2 b z 2 4 b -1 -1 n -1 p 2 c 2 v -1 2 s 2 2 b -1 q 0 n 2 q -1 n c v -1 2 s -1 p n -1 q p 2 c s -1 c v -1 2 b z q 1 -1 p 2 c s -1 c v -1 2 b z 2 b -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 -1 p 2 c s -1 c v -1 2 b z 2 4 b -1 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18