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/01.20.21.1303.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], "m"], RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["c", "2"]]], "+", SuperscriptBox["p", "2"]]], ")"]], "2"]], RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", 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SqrtBox["z"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "p"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], " ", SqrtBox["z"]]], "+", RowBox[List[SuperscriptBox["p", "2"], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["z"]]], "]"]]]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", 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"-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"]]], "+", SuperscriptBox["p", "2"]]], ")"]], "2"]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z cos m ( b z ) cosh ( c z ) z 1 ( p 2 - c 2 ) 2 ( 2 1 - m p z ( 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( ( p 2 ( p z - 1 ) - c 2 ( z p + 1 ) ) cosh ( c z ) - c ( - z c 2 - 2 p + p 2 z ) sinh ( c z ) ) ) + 2 1 - m p z k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( ( p 2 ( p z - 1 ) - ( - c + 2 b k - b m ) 2 ( z p + 1 ) ) cosh ( ( - c + 2 b k - b m ) z ) - ( - c + 2 b k - b m ) ( - z ( - c + 2 b k - b m ) 2 - 2 p + p 2 z ) sinh ( ( - c + 2 b k - b m ) z ) ) / ( p 2 - ( - c + 2 b k - b m ) 2 ) 2 + ( ( p 2 ( p z - 1 ) - ( c + 2 b k - b m ) 2 ( z p + 1 ) ) cosh ( ( c + 2 b k - b m ) z ) - ( c + 2 b k - b m ) ( - z ( c + 2 b k - b m ) 2 - 2 p + p 2 z ) sinh ( ( c + 2 b k - b m ) z ) ) / ( p 2 - ( c + 2 b k - b m ) 2 ) 2 ) /; m + Condition z p z 1 2 b z 1 2 m c z 1 2 1 p 2 -1 c 2 2 -1 2 1 -1 m p z 1 2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 p 2 p z 1 2 -1 -1 c 2 z 1 2 p 1 c z 1 2 -1 c -1 z 1 2 c 2 -1 2 p p 2 z 1 2 c z 1 2 2 1 -1 m p z 1 2 k 0 m -1 2 -1 Binomial m k p 2 p z 1 2 -1 -1 -1 c 2 b k -1 b m 2 z 1 2 p 1 -1 c 2 b k -1 b m z 1 2 -1 -1 c 2 b k -1 b m -1 z 1 2 -1 c 2 b k -1 b m 2 -1 2 p p 2 z 1 2 -1 c 2 b k -1 b m z 1 2 p 2 -1 -1 c 2 b k -1 b m 2 2 -1 p 2 p z 1 2 -1 -1 c 2 b k -1 b m 2 z 1 2 p 1 c 2 b k -1 b m z 1 2 -1 c 2 b k -1 b m -1 z 1 2 c 2 b k -1 b m 2 -1 2 p p 2 z 1 2 c 2 b k -1 b m z 1 2 p 2 -1 c 2 b k -1 b m 2 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18