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/01.20.21.1218.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sin[b z]^m Cosh[c z], z] == (Binomial[m, m/2] (1 - Mod[m, 2]) ((p Sqrt[Pi] (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)) (4 c^(3/2))) + (E^(p Sqrt[z]) Sinh[c z])/c))/2^m + (-I)^m 2^(-1 - m) Sum[(-1)^k Binomial[m, k] (-(E^(p Sqrt[z] - (c + I b (2 k - m)) z)/ (c + I b (2 k - m))) + E^(p Sqrt[z] + (c + I b (-2 k + m)) z)/ (c + I b (-2 k + m)) - (E^(p^2/(4 c + 8 I b k - 4 I b m)) p Sqrt[Pi] Erfi[(p - 2 (c + I b (2 k - m)) Sqrt[z])/ (2 Sqrt[-c + I b (-2 k + m)])])/(2 (-c + I b (-2 k + m))^(3/2)) + E^(I m Pi) (E^(p Sqrt[z] + (c + 2 I b k - I b m) z)/ (c + I b (2 k - m)) - (E^(p^2/(-4 c - 8 I b k + 4 I b m)) p Sqrt[Pi] Erfi[(p + 2 (c + 2 I b k - I b m) Sqrt[z])/ (2 Sqrt[c + I b (2 k - m)])])/(2 (c + I b (2 k - m))^(3/2))) + E^(I m Pi) (-(E^(p Sqrt[z] - (c - 2 I b k + I b m) z)/ (c + I b (-2 k + m))) - (E^(p^2/(4 c - 8 I b k + 4 I b m)) p Sqrt[Pi] Erfi[(p - 2 (c - 2 I b k + I b m) Sqrt[z])/ (2 Sqrt[-c + I b (2 k - m)])])/(2 (-c + I b (2 k - m))^(3/2))) - (E^(p^2/(-4 c + 8 I b k - 4 I b m)) p Sqrt[Pi] Erfi[(p + 2 (c + I b (-2 k + m)) Sqrt[z])/ (2 Sqrt[c + I b (-2 k + m)])])/(2 (c + I b (-2 k + m))^(3/2))), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

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SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], " ", SqrtBox["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["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18