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/01.20.21.1296.01

 Input Form

 Integrate[E^(p z) Cos[b z]^m Cosh[c Sqrt[z]], z] == 2^(-2 - m) Binomial[m, m/2] ((4 E^(p z) Cosh[c Sqrt[z]])/p - (c Sqrt[Pi] (Erfi[(c - 2 p Sqrt[z])/(2 Sqrt[p])] + Erfi[(c + 2 p Sqrt[z])/(2 Sqrt[p])]))/(E^(c^2/(4 p)) p^(3/2))) (1 - Mod[m, 2]) + 2^(-2 - m) Sum[Binomial[m, k] ((2 E^((-c) Sqrt[z] + ((-I) b (2 k - m) + p) z))/ ((-I) b (2 k - m) + p) + (2 E^(c Sqrt[z] + (I b (2 k - m) + p) z))/ (I b (2 k - m) + p) + (2 E^((-c) Sqrt[z] + ((-I) b (-2 k + m) + p) z))/ ((-I) b (-2 k + m) + p) + (2 E^(c Sqrt[z] + (I b (-2 k + m) + p) z))/ (I b (-2 k + m) + p) - (c Sqrt[Pi] Erfi[(c + 2 (I b (2 k - m) - p) Sqrt[z])/ (2 Sqrt[(-I) b (2 k - m) + p])])/ (E^(c^2/(4 ((-I) b (2 k - m) + p))) ((-I) b (2 k - m) + p)^(3/2)) - (c Sqrt[Pi] Erfi[(c + 2 (I b (-2 k + m) - p) Sqrt[z])/ (2 Sqrt[(-I) b (-2 k + m) + p])])/ (E^(c^2/(4 ((-I) b (-2 k + m) + p))) ((-I) b (-2 k + m) + p)^(3/2)) - (c Sqrt[Pi] Erfi[(c + 2 (I b (2 k - m) + p) Sqrt[z])/ (2 Sqrt[I b (2 k - m) + p])])/(E^(c^2/(4 (I b (2 k - m) + p))) (I b (2 k - m) + p)^(3/2)) - (c Sqrt[Pi] Erfi[(c + 2 (I b (-2 k + m) + p) Sqrt[z])/ (2 Sqrt[I b (-2 k + m) + p])])/(E^(c^2/(4 (I b (-2 k + m) + p))) (I b (-2 k + m) + p)^(3/2))), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

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RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], RowBox[List["3", "/", "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 2 - m - 2 ( 4 p z cosh ( c z ) p - c - c 2 4 p π ( erfi ( c + 2 p z 2 p ) + erfi ( c - 2 p z 2 p ) ) p 3 / 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 - c 2 4 ( p - b ( 2 k - m ) ) π erfi ( c + 2 ( b ( 2 k - m ) - p ) z 2 p - b ( 2 k - m ) ) ( p - b ( 2 k - m ) ) 3 / 2 + 2 ( p - b ( 2 k - m ) ) z - c z p - b ( 2 k - m ) + 2 z c + ( b ( 2 k - m ) + p ) z b ( 2 k - m ) + p - c - c 2 4 ( b ( 2 k - m ) + p ) π erfi ( c + 2 ( b ( 2 k - m ) + p ) z 2 b ( 2 k - m ) + p ) ( b ( 2 k - m ) + p ) 3 / 2 + 2 ( p - b ( m - 2 k ) ) z - c z p - b ( m - 2 k ) - c - c 2 4 ( p - b ( m - 2 k ) ) π erfi ( c + 2 ( b ( m - 2 k ) - p ) z 2 p - b ( m - 2 k ) ) ( p - b ( m - 2 k ) ) 3 / 2 + 2 z c + ( b ( m - 2 k ) + p ) z b ( m - 2 k ) + p - c - c 2 4 ( b ( m - 2 k ) + p ) π erfi ( c + 2 ( b ( m - 2 k ) + p ) z 2 b ( m - 2 k ) + p ) ( b ( m - 2 k ) + p ) 3 / 2 ) /; m + Condition z p z b z m c z 1 2 2 -1 m -2 4 p z c z 1 2 p -1 -1 c -1 c 2 4 p -1 1 2 Erfi c 2 p z 1 2 2 p 1 2 -1 Erfi c -1 2 p z 1 2 2 p 1 2 -1 p 3 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 c -1 c 2 4 p -1 b 2 k -1 m -1 1 2 Erfi c 2 b 2 k -1 m -1 p z 1 2 2 p -1 b 2 k -1 m 1 2 -1 p -1 b 2 k -1 m 3 2 -1 2 p -1 b 2 k -1 m z -1 c z 1 2 p -1 b 2 k -1 m -1 2 z 1 2 c b 2 k -1 m p z b 2 k -1 m p -1 -1 c -1 c 2 4 b 2 k -1 m p -1 1 2 Erfi c 2 b 2 k -1 m p z 1 2 2 b 2 k -1 m p 1 2 -1 b 2 k -1 m p 3 2 -1 2 p -1 b m -1 2 k z -1 c z 1 2 p -1 b m -1 2 k -1 -1 c -1 c 2 4 p -1 b m -1 2 k -1 1 2 Erfi c 2 b m -1 2 k -1 p z 1 2 2 p -1 b m -1 2 k 1 2 -1 p -1 b m -1 2 k 3 2 -1 2 z 1 2 c b m -1 2 k p z b m -1 2 k p -1 -1 c -1 c 2 4 b m -1 2 k p -1 1 2 Erfi c 2 b m -1 2 k p z 1 2 2 b m -1 2 k p 1 2 -1 b m -1 2 k p 3 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18