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/01.07.21.2544.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18