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/01.20.21.1292.01

 Input Form

 Integrate[E^(p Sqrt[z]) Cos[b z]^m Cosh[c z], z] == (Binomial[m, m/2] (1 - Mod[m, 2]) ((((p Sqrt[Pi])/(4 c^(3/2))) (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)) + (E^(p Sqrt[z]) Sinh[c z])/c))/2^m + 2^(-2 - m) Sum[Binomial[m, k] (-((2 E^(p Sqrt[z] - (c - I b (-2 k + m)) z))/(c + 2 I b k - I b m)) - (2 E^(p Sqrt[z] - (c - 2 I b k + I b m) z))/(c - 2 I b k + I b m) + (2 E^(p Sqrt[z] + (c - 2 I b k + I b m) z))/(c - 2 I b k + I b m) + (2 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 + 2 I b k - I b m) Sqrt[z])/ (2 Sqrt[-c + I b (-2 k + m)])])/(-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 - 2 I b k + I b m) Sqrt[z])/ (2 Sqrt[-c - I b (-2 k + m)])])/(-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)])])/(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)])])/(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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 MathML Form

 p z cos m ( b z ) cosh ( c z ) z 2 - m ( p π 4 c 3 / 2 - p 2 4 c ( p 2 2 c erf ( 2 c z - p 2 c ) - erfi ( 2 z c + p 2 c ) ) + 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 ) + 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]]]]] ( - p 2 4 c + 8 b k - 4 b m p π erfi ( p - 2 ( c + 2 b k - b m ) z 2 b ( m - 2 k ) - c ) ( b ( m - 2 k ) - c ) 3 / 2 + 2 z p + ( c - 2 b k + b m ) z c - 2 b k + b m - 2 p z - ( c - 2 b k + b m ) z c - 2 b k + b m - 2 p z - ( c - b ( m - 2 k ) ) z c + 2 b k - b m - 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 ) ) ( c + b ( m - 2 k ) ) 3 / 2 - p 2 4 c - 8 b k + 4 b m p π erfi ( p - 2 ( c - 2 b k + b m ) z 2 - c - b ( m - 2 k ) ) ( - c - b ( m - 2 k ) ) 3 / 2 + 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 ) ) ( c - b ( m - 2 k ) ) 3 / 2 ) /; m + Condition z p z 1 2 b z m c z 2 -1 m p 1 2 4 c 3 2 -1 -1 p 2 4 c -1 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 p z 1 2 c z c -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 p 2 4 c 8 b k -1 4 b m -1 p 1 2 Erfi p -1 2 c 2 b k -1 b m z 1 2 2 b m -1 2 k -1 c 1 2 -1 b m -1 2 k -1 c 3 2 -1 2 z 1 2 p c -1 2 b k b m z c -1 2 b k b m -1 -1 2 p z 1 2 -1 c -1 2 b k b m z c -1 2 b k b m -1 -1 2 p z 1 2 -1 c -1 b m -1 2 k z c 2 b k -1 b m -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 c b m -1 2 k 3 2 -1 -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 -1 c -1 b m -1 2 k 1 2 -1 -1 c -1 b m -1 2 k 3 2 -1 2 z 1 2 p c -1 b m -1 2 k z c -1 b m -1 2 k -1 -1 p 2 -4 c -1 8 b k 4 b m -1 p 1 2 Erfi 2 z 1 2 c -1 b m -1 2 k p 2 c -1 b m -1 2 k 1 2 -1 c -1 b m -1 2 k 3 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18