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/01.20.21.1225.01

 Input Form

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

 Standard Form

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

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

 Rule Form

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

 2002-12-18