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/01.20.21.1224.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sin[b z]^m Cosh[c Sqrt[z]], z] == (1/(-c^2 + p^2)^2) (2^(1 - m) E^(p Sqrt[z]) Binomial[m, m/2] (1 - Mod[m, 2]) ((-c^2 - p^2 - c^2 p Sqrt[z] + p^3 Sqrt[z]) Cosh[c Sqrt[z]] - c (-2 p - c^2 Sqrt[z] + p^2 Sqrt[z]) Sinh[c Sqrt[z]])) + 2^(-1 - m) Sum[(-1)^k Binomial[m, k] (E^((I m Pi)/2) ((I E^((-c + p) Sqrt[z] - I b (-2 k + m) z))/(b (-2 k + m)) - ((-c + p) Sqrt[Pi] Erfi[(-c + p - 2 I b (-2 k + m) Sqrt[z])/ (2 Sqrt[(-I) b (-2 k + m)])])/ (E^((I (-c + p)^2)/(4 b (-2 k + m))) (2 ((-I) b (-2 k + m))^ (3/2)))) + E^((I m Pi)/2) ((I E^((c + p) Sqrt[z] - I b (-2 k + m) z))/(b (-2 k + m)) - ((c + p) Sqrt[Pi] Erfi[(c + p - 2 I b (-2 k + m) Sqrt[z])/ (2 Sqrt[(-I) b (-2 k + m)])])/ (E^((I (c + p)^2)/(4 b (-2 k + m))) (2 ((-I) b (-2 k + m))^ (3/2)))) + (-((I E^((-c + p) Sqrt[z] + I b (-2 k + m) z))/ (b (-2 k + m))) - (E^((I (-c + p)^2)/(4 b (-2 k + m))) (-c + p) Sqrt[Pi] Erfi[(-c + p + 2 I b (-2 k + m) Sqrt[z])/ (2 Sqrt[I b (-2 k + m)])])/(2 (I b (-2 k + m))^(3/2)))/ E^((1/2) I m Pi) + (-((I E^((c + p) Sqrt[z] + I b (-2 k + m) z))/ (b (-2 k + m))) - (E^((I (c + p)^2)/(4 b (-2 k + m))) (c + p) Sqrt[Pi] Erfi[(c + p + 2 I b (-2 k + m) Sqrt[z])/ (2 Sqrt[I b (-2 k + m)])])/(2 (I b (-2 k + m))^(3/2)))/ E^((1/2) I m Pi)), {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 1 ( p 2 - c 2 ) 2 ( 2 1 - m p z ( 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 ) ( ( z p 3 - p 2 - c 2 z p - c 2 ) cosh ( c z ) - c ( - z c 2 - 2 p + p 2 z ) sinh ( c z ) ) ) + 2 - m - 1 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 ( ( p - c ) z - b ( m - 2 k ) z b ( m - 2 k ) - - ( p - c ) 2 4 b ( m - 2 k ) ( p - c ) π erfi ( - c + p - 2 b ( m - 2 k ) z 2 - b ( m - 2 k ) ) 2 ( - b ( m - 2 k ) ) 3 / 2 ) + m π 2 ( ( c + p ) z - b ( m - 2 k ) z b ( m - 2 k ) - - ( c + p ) 2 4 b ( m - 2 k ) ( c + p ) π erfi ( c + p - 2 b ( m - 2 k ) z 2 - b ( m - 2 k ) ) 2 ( - b ( m - 2 k ) ) 3 / 2 ) + - 1 2 m π ( - z ( p - c ) + b ( m - 2 k ) z b ( m - 2 k ) - ( p - c ) 2 4 b ( m - 2 k ) ( p - c ) π erfi ( - c + p + 2 b ( m - 2 k ) z 2 b ( m - 2 k ) ) 2 ( b ( m - 2 k ) ) 3 / 2 ) + - 1 2 m π ( - z ( c + p ) + b ( m - 2 k ) z b ( m - 2 k ) - ( c + p ) 2 4 b ( m - 2 k ) ( c + p ) π erfi ( c + p + 2 b ( m - 2 k ) z 2 b ( m - 2 k ) ) 2 ( b ( m - 2 k ) ) 3 / 2 ) ) /; m + Condition z p z 1 2 b z m c z 1 2 1 p 2 -1 c 2 2 -1 2 1 -1 m p z 1 2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 z 1 2 p 3 -1 p 2 -1 c 2 z 1 2 p -1 c 2 c z 1 2 -1 c -1 z 1 2 c 2 -1 2 p p 2 z 1 2 c z 1 2 2 -1 m -1 k 0 m -1 2 -1 -1 k Binomial m k m 2 -1 p -1 c z 1 2 -1 b m -1 2 k z b m -1 2 k -1 -1 -1 p -1 c 2 4 b m -1 2 k -1 p -1 c 1 2 Erfi -1 c p -1 2 b m -1 2 k z 1 2 2 -1 b m -1 2 k 1 2 -1 2 -1 b m -1 2 k 3 2 -1 m 2 -1 c p z 1 2 -1 b m -1 2 k z b m -1 2 k -1 -1 -1 c p 2 4 b m -1 2 k -1 c p 1 2 Erfi c p -1 2 b m -1 2 k z 1 2 2 -1 b m -1 2 k 1 2 -1 2 -1 b m -1 2 k 3 2 -1 -1 1 2 m -1 z 1 2 p -1 c b m -1 2 k z b m -1 2 k -1 -1 p -1 c 2 4 b m -1 2 k -1 p -1 c 1 2 Erfi -1 c p 2 b m -1 2 k z 1 2 2 b m -1 2 k 1 2 -1 2 b m -1 2 k 3 2 -1 -1 1 2 m -1 z 1 2 c p b m -1 2 k z b m -1 2 k -1 -1 c p 2 4 b m -1 2 k -1 c p 1 2 Erfi c p 2 b m -1 2 k z 1 2 2 b m -1 2 k 1 2 -1 2 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