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; }

 Cos

 http://functions.wolfram.com/01.07.21.2742.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18