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/01.07.21.2527.01

 Input Form

 Integrate[z^n Sin[b Sqrt[z]]^m Cos[c Sqrt[z]]^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) z^(1 + n) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] (Gamma[2 (1 + n), (-I) b (-2 k + m) Sqrt[z]]/(E^((1/2) I m Pi) ((-I) b (-2 k + m) Sqrt[z])^(2 (1 + n))) + (E^((I m Pi)/2) Gamma[2 (1 + n), I b (-2 k + m) Sqrt[z]])/ (I b (-2 k + m) Sqrt[z])^(2 (1 + n))), {k, 0, Floor[(1/2) (-1 + m)]}] - 2^(1 - m - v) z^(1 + n) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, s] (Gamma[2 (1 + n), (-I) c (-2 s + v) Sqrt[z]]/ ((-I) c (-2 s + v) Sqrt[z])^(2 (1 + n)) + Gamma[2 (1 + n), I c (-2 s + v) Sqrt[z]]/(I c (-2 s + v) Sqrt[z])^ (2 (1 + n))), {s, 0, Floor[(1/2) (-1 + v)]}] - 2^(1 - m - v) z^(1 + n) Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, s] (Gamma[2 (1 + n), ((-I) b (-2 k + m) - I c (-2 s + v)) Sqrt[z]]/(E^((1/2) I m Pi) (((-I) b (-2 k + m) - I c (-2 s + v)) Sqrt[z])^(2 (1 + n))) + (E^((I m Pi)/2) 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)) + Gamma[2 (1 + n), ((-I) b (-2 k + m) + I c (-2 s + v)) Sqrt[z]]/(E^((1/2) I m Pi) (((-I) b (-2 k + m) + I c (-2 s + v)) Sqrt[z])^(2 (1 + n))) + (E^((I m Pi)/2) 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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"\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z n sin m ( z b ) cos v ( z c ) z - 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 ) ( 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]]]]] ( - 1 2 m π Γ ( 2 ( n + 1 ) , - b ( m - 2 k ) z ) ( - b ( m - 2 k ) z ) - 2 ( n + 1 ) + m π 2 ( b ( m - 2 k ) z ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , b ( m - 2 k ) z ) ) ) z n + 1 - 2 - m - v + 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]]]]] ( Γ ( 2 ( n + 1 ) , - c ( v - 2 s ) z ) ( - c ( v - 2 s ) z ) - 2 ( n + 1 ) + ( c ( v - 2 s ) z ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , c ( v - 2 s ) z ) ) ) z n + 1 - 2 - m - v + 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 m π 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 ) + m π 2 ( ( 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 m π ( ( - 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 ) + m π 2 ( ( 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 ) ) ) z n + 1 + 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 /; n m + v + Condition z z n z 1 2 b m z 1 2 c v -1 2 -1 m -1 v 1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k Binomial m k -1 1 2 m Gamma 2 n 1 -1 b m -1 2 k z 1 2 -1 b m -1 2 k z 1 2 -2 n 1 m 2 -1 b m -1 2 k z 1 2 -2 n 1 Gamma 2 n 1 b m -1 2 k z 1 2 z n 1 -1 2 -1 m -1 v 1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 Binomial v s Gamma 2 n 1 -1 c v -1 2 s z 1 2 -1 c v -1 2 s z 1 2 -2 n 1 c v -1 2 s z 1 2 -2 n 1 Gamma 2 n 1 c v -1 2 s z 1 2 z n 1 -1 2 -1 m -1 v 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 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 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 -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 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 z n 1 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 n m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18