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/01.20.21.1290.01

 Input Form

 Integrate[E^(p Sqrt[z]) Cos[b Sqrt[z]]^m Cosh[c z], z] == (Binomial[m, m/2] (1 - Mod[m, 2]) ((((p Sqrt[Pi])/(4 c^(3/2))) (E^(p^2/(2 c)) Erf[(-p + 2 c Sqrt[z])/(2 Sqrt[c])] - Erfi[(p + 2 c Sqrt[z])/(2 Sqrt[c])]))/E^(p^2/(4 c)) + (E^(p Sqrt[z]) Sinh[c z])/c))/2^m + 2^(-2 - m) Sum[Binomial[m, k] ((8 E^(p Sqrt[z]) Cos[b (2 k - m) Sqrt[z]] Sinh[c z])/c + (1/(-c)^(5/2)) (c E^(((-I) b (-2 k + m) + p)^2/(4 c)) ((-I) b (-2 k + m) + p) Sqrt[Pi] Erfi[((-I) b (-2 k + m) + p - 2 c Sqrt[z])/(2 Sqrt[-c])]) + (1/(-c)^(5/2)) (c E^((I b (-2 k + m) + p)^2/(4 c)) (I b (-2 k + m) + p) Sqrt[Pi] Erfi[(I b (-2 k + m) + p - 2 c Sqrt[z])/(2 Sqrt[-c])]) - (1/c^(3/2)) (E^((b (-2 k + m) + I p)^2/(4 c)) ((-I) b (-2 k + m) + p) Sqrt[Pi] Erfi[((-I) b (-2 k + m) + p + 2 c Sqrt[z])/(2 Sqrt[c])]) - (1/c^(3/2)) (((I b (-2 k + m) + p) Sqrt[Pi] Erfi[(I b (-2 k + m) + p + 2 c Sqrt[z])/(2 Sqrt[c])])/ E^((I b (-2 k + m) + p)^2/(4 c)))), {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", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["-", "m"]]], 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[FractionBox[RowBox[List["p", " ", SqrtBox["\[Pi]"], " "]], RowBox[List["4", " ", SuperscriptBox["c", RowBox[List["3", "/", "2"]]]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], RowBox[List["(", 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 MathML Form

 p z cos m ( b z ) cosh ( c z ) z 2 - m ( p π 4 c 3 / 2 - p 2 4 c ( p 2 2 c erf ( 2 c z - p 2 c ) - erfi ( 2 z c + p 2 c ) ) + p z sinh ( c z ) c ) ( 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 - b ( m - 2 k ) ) 2 4 c ( p - b ( m - 2 k ) ) π erfi ( - 2 z c - b ( m - 2 k ) + p 2 - c ) ( - c ) 5 / 2 + c ( b ( m - 2 k ) + p ) 2 4 c ( b ( m - 2 k ) + p ) π erfi ( - 2 z c + b ( m - 2 k ) + p 2 - c ) ( - c ) 5 / 2 - ( b ( m - 2 k ) + p ) 2 4 c ( p - b ( m - 2 k ) ) π erfi ( 2 z c - b ( m - 2 k ) + p 2 c ) c 3 / 2 - - ( b ( m - 2 k ) + p ) 2 4 c ( b ( m - 2 k ) + p ) π erfi ( 2 z c + b ( m - 2 k ) + p 2 c ) c 3 / 2 + 8 p z cos ( b ( 2 k - m ) z ) sinh ( c z ) c ) /; m + Condition z p z 1 2 b z 1 2 m c z 2 -1 m p 1 2 4 c 3 2 -1 -1 p 2 4 c -1 p 2 2 c -1 Erf 2 c z 1 2 -1 p 2 c 1 2 -1 -1 Erfi 2 z 1 2 c p 2 c 1 2 -1 p z 1 2 c z c -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 2 -1 m -2 k 0 m -1 2 -1 Binomial m k c p -1 b m -1 2 k 2 4 c -1 p -1 b m -1 2 k 1 2 Erfi -2 z 1 2 c -1 b m -1 2 k p 2 -1 c 1 2 -1 -1 c 5 2 -1 c b m -1 2 k p 2 4 c -1 b m -1 2 k p 1 2 Erfi -2 z 1 2 c b m -1 2 k p 2 -1 c 1 2 -1 -1 c 5 2 -1 -1 b m -1 2 k p 2 4 c -1 p -1 b m -1 2 k 1 2 Erfi 2 z 1 2 c -1 b m -1 2 k p 2 c 1 2 -1 c 3 2 -1 -1 -1 b m -1 2 k p 2 4 c -1 b m -1 2 k p 1 2 Erfi 2 z 1 2 c b m -1 2 k p 2 c 1 2 -1 c 3 2 -1 8 p z 1 2 b 2 k -1 m z 1 2 c z c -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18