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/01.20.21.1220.01

 Input Form

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

 Rule Form

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

 2002-12-18