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/01.07.21.2766.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18