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/01.20.21.1298.01

 Input Form

 Integrate[E^(p Sqrt[z]) Cos[b z]^m Cosh[c Sqrt[z]], z] == (E^((c + p) Sqrt[z]) (-(1/(-c - p)^2) + (-1 - c Sqrt[z] + p Sqrt[z])/ (E^(2 c Sqrt[z]) (-c + p)^2) + Sqrt[z]/(c + p)) Binomial[m, m/2] (1 - Mod[m, 2]))/2^m + 2^(-2 - m) Sum[Binomial[m, k] ((8 E^(p Sqrt[z]) Cosh[c Sqrt[z]] Sin[2 b k z - b m z])/(2 b k - b m) - ((c + p) Sqrt[Pi] Erfi[(c + p - 2 I b (2 k - m) Sqrt[z])/ (2 Sqrt[(-I) b (2 k - m)])])/(E^((I (c + p)^2)/(b (8 k - 4 m))) ((-I) b (2 k - m))^(3/2)) + (E^((I (c - p)^2)/(b (8 k - 4 m))) (c - p) Sqrt[Pi] Erfi[(-c + p + 2 I b (2 k - m) Sqrt[z])/ (2 Sqrt[I b (2 k - m)])])/(I b (2 k - m))^(3/2) + (E^((I (c + p)^2)/(b (8 k - 4 m))) Sqrt[(-I) b (-2 k + m)] (c + p) Sqrt[Pi] Erfi[(c + p - 2 I b (-2 k + m) Sqrt[z])/ (2 Sqrt[(-I) b (-2 k + m)])])/(b^2 (-2 k + m)^2) - (1/(b^2 (-2 k + m)^2)) (E^((I (c - p)^2)/(4 b (-2 k + m))) Sqrt[I b (-2 k + m)] (c - p) Sqrt[Pi] Erfi[(-c + p + 2 I b (-2 k + m) Sqrt[z])/ (2 Sqrt[I b (-2 k + m)])])), {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", " ", "z"]], "]"]], "m"], RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "p"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", SqrtBox["z"]]]]], ")"]]]], 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" ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], "]"]]]], RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], "2"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]], "2"]]], RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]], " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", "p", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z cos m ( b z ) cosh ( c z ) z 2 - m ( c + p ) z ( - 2 c z ( - z c + p z - 1 ) ( p - c ) 2 + z c + p - 1 ( - c - p ) 2 ) ( 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 ) + 2 - m - 2 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]]]]] ( - - ( c + p ) 2 b ( 8 k - 4 m ) ( c + p ) π erfi ( c + p - 2 b ( 2 k - m ) z 2 - b ( 2 k - m ) ) ( - b ( 2 k - m ) ) 3 / 2 + ( c - p ) 2 b ( 8 k - 4 m ) ( c - p ) π erfi ( - c + p + 2 b ( 2 k - m ) z 2 b ( 2 k - m ) ) ( b ( 2 k - m ) ) 3 / 2 + ( c + p ) 2 b ( 8 k - 4 m ) - b ( m - 2 k ) ( c + p ) π erfi ( c + p - 2 b ( m - 2 k ) z 2 - b ( m - 2 k ) ) b 2 ( m - 2 k ) 2 - ( c - p ) 2 4 b ( m - 2 k ) b ( m - 2 k ) ( c - p ) π erfi ( - c + p + 2 b ( m - 2 k ) z 2 b ( m - 2 k ) ) b 2 ( m - 2 k ) 2 + 8 p z cosh ( c z ) sin ( 2 b k z - b m z ) 2 b k - b m ) /; m + Condition z p z 1 2 b z m c z 1 2 2 -1 m c p z 1 2 -2 c z 1 2 -1 z 1 2 c p z 1 2 -1 p -1 c 2 -1 z 1 2 c p -1 -1 1 -1 c -1 p 2 -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 2 -1 m -2 k 0 m -1 2 -1 Binomial m k -1 -1 c p 2 b 8 k -1 4 m -1 c p 1 2 Erfi c p -1 2 b 2 k -1 m z 1 2 2 -1 b 2 k -1 m 1 2 -1 -1 b 2 k -1 m 3 2 -1 c -1 p 2 b 8 k -1 4 m -1 c -1 p 1 2 Erfi -1 c p 2 b 2 k -1 m z 1 2 2 b 2 k -1 m 1 2 -1 b 2 k -1 m 3 2 -1 c p 2 b 8 k -1 4 m -1 -1 b m -1 2 k 1 2 c p 1 2 Erfi c p -1 2 b m -1 2 k z 1 2 2 -1 b m -1 2 k 1 2 -1 b 2 m -1 2 k 2 -1 -1 c -1 p 2 4 b m -1 2 k -1 b m -1 2 k 1 2 c -1 p 1 2 Erfi -1 c p 2 b m -1 2 k z 1 2 2 b m -1 2 k 1 2 -1 b 2 m -1 2 k 2 -1 8 p z 1 2 c z 1 2 2 b k z -1 b m z 2 b k -1 b m -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18