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/01.20.21.1376.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Sin[d + c z]^m Cosh[a z], z] == 2^(-1 - m) z^\[Alpha] ((Binomial[m, m/2] (-1 + Mod[m, 2]) (((-(a + p)) z)^\[Alpha] Gamma[\[Alpha], (a - p) z] + ((a - p) z)^\[Alpha] Gamma[\[Alpha], (-(a + p)) z]))/ (((a - p) z)^\[Alpha] ((-(a + p)) z)^\[Alpha]) - Sum[((-1)^k Binomial[m, k] (((a + I c (2 k - m) - p) z)^\[Alpha] ((-(a + I c (2 k - m) + p)) z)^\[Alpha] ((-(a - 2 I c k + I c m + p)) z)^\[Alpha] Gamma[\[Alpha], (a + I c (-2 k + m) - p) z] (Cos[(1/2) (4 d k - 2 d m + m Pi)] + I Sin[(1/2) (4 d k - 2 d m + m Pi)]) + ((a + I c (-2 k + m) - p) z)^\[Alpha] (((-(a + I c (2 k - m) + p)) z)^\[Alpha] (Cos[d (-2 k + m) - (m Pi)/2] + I Sin[d (-2 k + m) - (m Pi)/2]) (((-(a - 2 I c k + I c m + p)) z)^\[Alpha] Gamma[\[Alpha], (a + 2 I c k - I c m - p) z] + ((a + 2 I c k - I c m - p) z)^ \[Alpha] Gamma[\[Alpha], (-(a - 2 I c k + I c m + p)) z]) + ((a + I c (2 k - m) - p) z)^\[Alpha] ((-(a - 2 I c k + I c m + p)) z)^\[Alpha] Gamma[\[Alpha], (-(a + I c (2 k - m) + p)) z] (Cos[(1/2) (4 d k - 2 d m + m Pi)] + I Sin[(1/2) (4 d k - 2 d m + m Pi)]))))/ (((a + I c (2 k - m) - p) z)^\[Alpha] ((a + I c (-2 k + m) - p) z)^ \[Alpha] ((-(a + I c (2 k - m) + p)) z)^\[Alpha] ((-(a - 2 I c k + I c m + p)) z)^\[Alpha]), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z α - 1 p z sin m ( d + c z ) cosh ( a z ) z 2 - m - 1 z α ( ( ( a - p ) z ) - α ( - ( a + p ) z ) - α ( 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]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) ( Γ ( α , - ( a + p ) z ) ( ( a - p ) z ) α + ( - ( a + p ) z ) α Γ ( α , ( a - p ) z ) ) - k = 0 m - 1 2 ( - 1 ) k ( ( a + c ( 2 k - m ) - p ) z ) - α ( ( a + c ( m - 2 k ) - p ) z ) - α ( - ( a + c ( 2 k - m ) + p ) z ) - α ( - ( a - 2 c k + c m + p ) z ) - α ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( ( Γ ( α , - ( a - 2 c k + c m + p ) z ) ( ( a + 2 c k - c m - p ) z ) α + ( - ( a - 2 c k + c m + p ) z ) α Γ ( α , ( a + 2 c k - c m - p ) z ) ) ( cos ( d ( m - 2 k ) - m π 2 ) + sin ( d ( m - 2 k ) - m π 2 ) ) ( - ( a + c ( 2 k - m ) + p ) z ) α + ( ( a + c ( 2 k - m ) - p ) z ) α ( - ( a - 2 c k + c m + p ) z ) α Γ ( α , - ( a + c ( 2 k - m ) + p ) z ) ( cos ( 1 2 ( 4 d k - 2 d m + m π ) ) + sin ( 1 2 ( 4 d k - 2 d m + m π ) ) ) ) ( ( a + c ( m - 2 k ) - p ) z ) α + ( ( a + c ( 2 k - m ) - p ) z ) α ( - ( a + c ( 2 k - m ) + p ) z ) α ( - ( a - 2 c k + c m + p ) z ) α Γ ( α , ( a + c ( m - 2 k ) - p ) z ) ( cos ( 1 2 ( 4 d k - 2 d m + m π ) ) + sin ( 1 2 ( 4 d k - 2 d m + m π ) ) ) ) ) /; m + Condition z z α -1 p z d c z m a z 2 -1 m -1 z α a -1 p z -1 α -1 a p z -1 α Binomial m m 2 -1 \$CellContext`m 2 -1 Gamma α -1 a p z a -1 p z α -1 a p z α Gamma α a -1 p z -1 k 0 m -1 2 -1 -1 k a c 2 k -1 m -1 p z -1 α a c m -1 2 k -1 p z -1 α -1 a c 2 k -1 m p z -1 α -1 a -1 2 c k c m p z -1 α Binomial m k Gamma α -1 a -1 2 c k c m p z a 2 c k -1 c m -1 p z α -1 a -1 2 c k c m p z α Gamma α a 2 c k -1 c m -1 p z d m -1 2 k -1 m 2 -1 d m -1 2 k -1 m 2 -1 -1 a c 2 k -1 m p z α a c 2 k -1 m -1 p z α -1 a -1 2 c k c m p z α Gamma α -1 a c 2 k -1 m p z 1 2 4 d k -1 2 d m m 1 2 4 d k -1 2 d m m a c m -1 2 k -1 p z α a c 2 k -1 m -1 p z α -1 a c 2 k -1 m p z α -1 a -1 2 c k c m p z α Gamma α a c m -1 2 k -1 p z 1 2 4 d k -1 2 d m m 1 2 4 d k -1 2 d m m m SuperPlus [/itex]

 Rule Form

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

 2002-12-18