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/01.07.21.2462.01

 Input Form

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

 Standard Form

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 MathML Form

 z α - 1 sin ( b z r + e ) cos v ( c z r + g ) z - r 2 - v - 1 ( 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]]]]] ( - e ( b z r ) - α r Γ ( α r , b z r ) - e ( - b z r ) - α r Γ ( α r , - b z r ) ) ( 1 - v mod 2 \$CellContext`v 2 ) z α - 1 r 2 - v - 1 z α 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 - g ( v - 2 s ) Γ ( α r , ( - b + c ( v - 2 s ) ) z r ) ( ( - b + c ( v - 2 s ) ) z r ) - α r + - e - g ( v - 2 s ) ( ( b + c ( v - 2 s ) ) z r ) - α r Γ ( α r , ( b + c ( v - 2 s ) ) z r ) - e + g ( v - 2 s ) ( ( - b - c ( v - 2 s ) ) z r ) - α r Γ ( α r , ( - b - c ( v - 2 s ) ) z r ) + - e + g ( v - 2 s ) ( ( b - c ( v - 2 s ) ) z r ) - α r Γ ( α r , ( b - c ( v - 2 s ) ) z r ) ) /; v + Condition z z α -1 b z r e c z r g v -1 r -1 2 -1 v -1 Binomial v v 2 -1 -1 e b z r -1 α r -1 Gamma α r -1 b z r -1 e -1 b z r -1 α r -1 Gamma α r -1 -1 b z r 1 -1 \$CellContext`v 2 z α -1 1 r -1 2 -1 v -1 z α s 0 v -1 2 -1 Binomial v s -1 e -1 g v -1 2 s Gamma α r -1 -1 b c v -1 2 s z r -1 b c v -1 2 s z r -1 α r -1 -1 e -1 g v -1 2 s b c v -1 2 s z r -1 α r -1 Gamma α r -1 b c v -1 2 s z r -1 e g v -1 2 s -1 b -1 c v -1 2 s z r -1 α r -1 Gamma α r -1 -1 b -1 c v -1 2 s z r -1 e g v -1 2 s b -1 c v -1 2 s z r -1 α r -1 Gamma α r -1 b -1 c v -1 2 s z r v SuperPlus [/itex]

 Rule Form

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

 2002-12-18