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/01.20.21.4822.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], RowBox[List["Sinh", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List["-", "v"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", "p"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "p"]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", "p", "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", "p", "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "p", "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "p", "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]], ",", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]]]], ")"]]]]]]]]]]]], "/;", 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 sinh ( b z ) cosh v ( c z ) z - 2 - v ( 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 - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - p ) z ) - ( b - p ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - p ) z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( Γ ( 2 ( n + 1 ) , ( - b - p + c ( v - 2 s ) ) z ) ( - b - p + c ( v - 2 s ) ) - 2 ( n + 1 ) - ( b - p + c ( v - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - p + c ( v - 2 s ) ) z ) + ( - b - p - c ( v - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( - b - p - c ( v - 2 s ) ) z ) - ( b - p - c ( v - 2 s ) ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , ( b - p - c ( v - 2 s ) ) z ) ) /; v + n Condition z z n p z 1 2 b z 1 2 c z 1 2 v -1 2 -1 v Binomial v v 2 -1 -1 b -1 p -2 n 1 Gamma 2 n 1 -1 b -1 p z 1 2 -1 b -1 p -2 n 1 Gamma 2 n 1 b -1 p z 1 2 1 -1 \$CellContext`v 2 -1 2 -1 v s 0 v -1 2 -1 Binomial v s Gamma 2 n 1 -1 b -1 p c v -1 2 s z 1 2 -1 b -1 p c v -1 2 s -2 n 1 -1 b -1 p c v -1 2 s -2 n 1 Gamma 2 n 1 b -1 p c v -1 2 s z 1 2 -1 b -1 p -1 c v -1 2 s -2 n 1 Gamma 2 n 1 -1 b -1 p -1 c v -1 2 s z 1 2 -1 b -1 p -1 c v -1 2 s -2 n 1 Gamma 2 n 1 b -1 p -1 c v -1 2 s z 1 2 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18