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/01.20.21.1216.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sin[b Sqrt[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^((I b (-2 k + m) + p) Sqrt[z] - c z)/c) + E^((I b (-2 k + m) + p) Sqrt[z] + c z)/c + E^(I m Pi) (-(E^((2 I b k - I b m + p) Sqrt[z] - c z)/c) - (1/(2 (-c)^(3/2))) (E^((2 I b k - I b m + p)^2/(4 c)) (2 I b k - I b m + p) Sqrt[Pi] Erfi[(2 I b k - I b m + p - 2 c Sqrt[z])/(2 Sqrt[-c])])) - (1/(2 (-c)^(3/2))) (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])]) + E^(I m Pi) (E^((2 I b k - I b m + p) Sqrt[z] + c z)/c - (1/(2 c^(3/2))) (((2 I b k - I b m + p) Sqrt[Pi] Erfi[(2 I b k - I b m + p + 2 c Sqrt[z])/(2 Sqrt[c])])/ E^((2 I b k - I b m + p)^2/(4 c)))) - (1/(2 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

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 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 ( - ( 2 b k - b m + p ) 2 4 c ( 2 b k - b m + p ) π erfi ( - 2 z c + 2 b k - b m + p 2 - c ) 2 ( - c ) 3 / 2 - ( 2 b k - b m + p ) z - c z c ) + z ( b ( m - 2 k ) + p ) + c z 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 ) 2 ( - c ) 3 / 2 + m π ( z ( 2 b k - b m + p ) + c z c - - ( 2 b k - b m + p ) 2 4 c ( 2 b k - b m + p ) π erfi ( 2 z c + 2 b k - b m + p 2 c ) 2 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 ) 2 c 3 / 2 - ( b ( m - 2 k ) + p ) z - c z c ) + 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 1 2 m c z 2 -1 m -1 -1 m k 0 m -1 2 -1 -1 k Binomial m k m -1 2 b k -1 b m p 2 4 c -1 2 b k -1 b m p 1 2 Erfi -2 z 1 2 c 2 b k -1 b m p 2 -1 c 1 2 -1 2 -1 c 3 2 -1 -1 2 b k -1 b m p z 1 2 -1 c z c -1 z 1 2 b m -1 2 k p c z c -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 -1 c 1 2 -1 2 -1 c 3 2 -1 m z 1 2 2 b k -1 b m p c z c -1 -1 -1 2 b k -1 b m p 2 4 c -1 2 b k -1 b m p 1 2 Erfi 2 z 1 2 c 2 b k -1 b m p 2 c 1 2 -1 2 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 2 c 3 2 -1 -1 b m -1 2 k p z 1 2 -1 c z c -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