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/01.20.21.1223.01

 Input Form

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

 Standard Form

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FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", "p"]]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z 2 sin m ( b z ) cosh ( c z 2 ) z 2 - m - 2 π ( 1 - m mod 2 \$CellContext`m 2 ) ( p - c ) ( c + p ) ( 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]]]]] ( p - c ( c + p ) erfi ( 2 p z - 2 c z 2 p - c ) + ( p - c ) c + p erfi ( c + p z ) ) + 2 - m - 2 π k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 ( p - c ) ( c + p ) ( - 2 m ( p - c ) π - b 2 ( 2 k - m ) 2 4 ( p - c ) p - c ( c + p ) erfi ( - b ( 2 k - m ) - 2 c z + 2 p z 2 p - c ) + - - b 2 ( 2 k - m ) 2 - 2 m ( c + p ) π 4 ( c + p ) ( p - c ) c + p erfi ( b ( 2 k - m ) + 2 ( c + p ) z 2 c + p ) ) + 1 ( p - c ) ( c + p ) ( - - b 2 ( m - 2 k ) 2 - 2 m ( p - c ) π 4 ( p - c ) p - c ( c + p ) erfi ( - b ( m - 2 k ) - 2 c z + 2 p z 2 p - c ) + - 2 m ( c + p ) π - b 2 ( m - 2 k ) 2 4 ( c + p ) ( p - c ) c + p erfi ( b ( m - 2 k ) + 2 ( c + p ) z 2 c + p ) ) ) /; m + Condition z p z 2 b z m c z 2 2 -1 m -2 1 2 1 -1 \$CellContext`m 2 p -1 c c p -1 Binomial m m 2 -1 p -1 c 1 2 c p Erfi 2 p z -1 2 c z 2 p -1 c 1 2 -1 p -1 c c p 1 2 Erfi c p 1 2 z 2 -1 m -2 1 2 k 0 m -1 2 -1 -1 k Binomial m k 1 p -1 c c p -1 -1 2 m p -1 c -1 b 2 2 k -1 m 2 4 p -1 c -1 p -1 c 1 2 c p Erfi -1 b 2 k -1 m -1 2 c z 2 p z 2 p -1 c 1 2 -1 -1 -1 b 2 2 k -1 m 2 -1 2 m c p 4 c p -1 p -1 c c p 1 2 Erfi b 2 k -1 m 2 c p z 2 c p 1 2 -1 1 p -1 c c p -1 -1 -1 b 2 m -1 2 k 2 -1 2 m p -1 c 4 p -1 c -1 p -1 c 1 2 c p Erfi -1 b m -1 2 k -1 2 c z 2 p z 2 p -1 c 1 2 -1 -1 2 m c p -1 b 2 m -1 2 k 2 4 c p -1 p -1 c c p 1 2 Erfi b m -1 2 k 2 c p z 2 c p 1 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18