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/01.07.21.2769.01

 Input Form

 Integrate[z^n E^(b z^2 + d z + e) Sin[a z^2 + p z + q]^m Cos[c z^2 + f z + g]^v, z] == (2^(-1 - m - v) b^(-1 - n) ((-E^e) Binomial[m, m/2] Binomial[v, v/2] (-1 + Mod[m, 2]) (-1 + Mod[v, 2]) Sum[2^(j - n) (-d)^(-j + n) (d + 2 b z)^(1 + j) (-((d + 2 b z)^2/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + 2 b z)^2/(4 b))], {j, 0, n}] + b^(1 + n) E^(d^2/(4 b)) (Binomial[v, v/2] (-1 + Mod[v, 2]) Sum[(-1)^k Binomial[m, k] (E^(e + (I d + (-2 k + m) p)^2/(4 (b + I a (2 k - m))) + (I m Pi)/2 + I (2 k - m) q) (b + I a (2 k - m))^(-1 - n) Sum[2^(j - n) (-d - 2 I k p + I m p)^ (-j + n) (d + I (2 k - m) p + 2 (b + I a (2 k - m)) z)^(1 + j) (-((d + I (2 k - m) p + 2 (b + I a (2 k - m)) z)^2/ (b + I a (2 k - m))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I (2 k - m) p + 2 (b + I a (2 k - m)) z)^2/(4 (b + I a (2 k - m))))], {j, 0, n}] + E^(e - (d + I (-2 k + m) p)^2/(4 (b + I a (-2 k + m))) - (I m Pi)/2 + I (-2 k + m) q) (b + I a (-2 k + m))^(-1 - n) Sum[2^(j - n) (-d - I (-2 k + m) p)^(-j + n) (d + I (-2 k + m) p + 2 (b + I a (-2 k + m)) z)^(1 + j) (-((d + I (-2 k + m) p + 2 (b + I a (-2 k + m)) z)^2/ (b + I a (-2 k + m))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I (-2 k + m) p + 2 (b + I a (-2 k + m)) z)^2/(4 (b + I a (-2 k + m))))], {j, 0, n}]), {k, 0, Floor[(1/2) (-1 + m)]}] + Binomial[m, m/2] (-1 + Mod[m, 2]) Sum[Binomial[v, s] (E^(e + I g (2 s - v) + (I d - 2 f s + f v)^2/(4 (b + 2 I c s - I c v))) (b + 2 I c s - I c v)^(-1 - n) Sum[2^(j - n) (-d - 2 I f s + I f v)^(-j + n) (d + I f (2 s - v) + 2 (b + 2 I c s - I c v) z)^(1 + j) (-((d + I f (2 s - v) + 2 (b + 2 I c s - I c v) z)^2/ (b + 2 I c s - I c v)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I f (2 s - v) + 2 (b + 2 I c s - I c v) z)^2/(4 (b + 2 I c s - I c v)))], {j, 0, n}] + E^(e + I g (-2 s + v) - (d + I f (-2 s + v))^2/(4 (b + I c (-2 s + v)))) (b + I c (-2 s + v))^(-1 - n) Sum[2^(j - n) (-d - I f (-2 s + v))^(-j + n) (d + I f (-2 s + v) + 2 (b + I c (-2 s + v)) z)^(1 + j) (-((d + I f (-2 s + v) + 2 (b + I c (-2 s + v)) z)^2/ (b + I c (-2 s + v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I f (-2 s + v) + 2 (b + I c (-2 s + v)) z)^2/(4 (b + I c (-2 s + v))))], {j, 0, n}]), {s, 0, Floor[(1/2) (-1 + v)]}] - Sum[(-1)^k Binomial[m, k] Sum[(Binomial[v, s] (E^((1/4) I (8 g (2 s - v) + (I d + 2 k p - m p - 2 f s + f v)^2/(I b + 2 a k - a m - 2 c s + c v))) (b - I (2 a k - a m - 2 c s + c v))^(-1 - n) Sum[2^(j - n) (-d + I (2 k p - m p - 2 f s + f v))^ (-j + n) ((I d + 2 k p - m p - 2 f s + f v + 2 I b z + 4 a k z - 2 a m z - 4 c s z + 2 c v z)^2/(b - I (2 a k - a m - 2 c s + c v)))^((1/2) (-1 - j)) (d - I (-2 f s + f v + 2 I b z - 4 c s z + 2 c v z + 2 k (p + 2 a z) - m (p + 2 a z)))^(1 + j) Binomial[n, j] Gamma[(1 + j)/2, (I (I d + 2 k p - m p - 2 f s + f v + 2 I b z + 4 a k z - 2 a m z - 4 c s z + 2 c v z)^2)/ (4 (I b + 2 a k - a m - 2 c s + c v))], {j, 0, n}] + ((b + I a (-2 k + m) + I c (-2 s + v))^(-1 - n) Sum[ 2^(j - n) (-d + I (2 k p - m p + 2 f s - f v))^(-j + n) (d + I (-2 k + m) p + I f (-2 s + v) + 2 (b + I a (-2 k + m) + I c (-2 s + v)) z)^(1 + j) (-((d + I (-2 k + m) p + I f (-2 s + v) + 2 (b + I a (-2 k + m) + I c (-2 s + v)) z)^2/(b + I a (-2 k + m) + I c (-2 s + v))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((d + I (-2 k + m) p + I f (-2 s + v) + 2 (b + I a (-2 k + m) + I c (-2 s + v)) z)^2/(4 (b + I a (-2 k + m) + I c (-2 s + v))))], {j, 0, n}])/E^((d + I (-2 k + m) p + I f (-2 s + v))^2/(4 (b + I a (-2 k + m) + I c (-2 s + v)))) + E^(I (m Pi + 4 k q - 2 m q)) (((b + I (2 a k - a m - 2 c s + c v))^(-1 - n) Sum[2^(j - n) (-d + I (-2 k p + m p + 2 f s - f v))^(-j + n) ((I d + m p + 2 f s - f v + 2 I b z + 2 a m z + 4 c s z - 2 c v z - 2 k (p + 2 a z))^2/(b + I (2 a k - a m - 2 c s + c v)))^((1/2) (-1 - j)) (d + I (-2 f s + f v - 2 I b z - 4 c s z + 2 c v z + 2 k (p + 2 a z) - m (p + 2 a z)))^(1 + j) Binomial[n, j] Gamma[ (1 + j)/2, -((I (I d + m p + 2 f s - f v + 2 I b z + 2 a m z + 4 c s z - 2 c v z - 2 k (p + 2 a z))^2)/ (4 ((-I) b + 2 a k - a m - 2 c s + c v)))], {j, 0, n}])/ E^((I (I d - 2 k p + m p + 2 f s - f v)^2)/(4 ((-I) b + 2 a k - a m - 2 c s + c v))) + E^((1/4) I (8 g (2 s - v) + (I d - 2 k p + m p - 2 f s + f v)^2/ (I b - 2 a k + a m - 2 c s + c v))) (b + I (2 a k - a m + 2 c s - c v))^(-1 - n) Sum[2^(j - n) (-d - I (2 k p - m p + 2 f s - f v))^(-j + n) ((I d + m p - 2 f s + f v + 2 I b z + 2 a m z - 4 c s z + 2 c v z - 2 k (p + 2 a z))^2/(b + I (2 a k - a m + 2 c s - c v)))^((1/2) (-1 - j)) (d + I (2 f s - f v - 2 I b z + 4 c s z - 2 c v z + 2 k (p + 2 a z) - m (p + 2 a z)))^(1 + j) Binomial[n, j] Gamma[(1 + j)/2, (I (I d + m p - 2 f s + f v + 2 I b z + 2 a m z - 4 c s z + 2 c v z - 2 k (p + 2 a z))^2)/ (4 (I b - 2 a k + a m - 2 c s + c v))], {j, 0, n}])))/ E^((1/2) I (2 I e + m Pi + 4 k q - 2 m q + 4 g s - 2 g v)), {s, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}])))/ E^(d^2/(4 b)) /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0

 Standard Form

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RowBox[List["p", "+", RowBox[List["2", " ", "a", " ", "z"]]]], ")"]]]]]], ")"]], "2"]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", RowBox[List["2", " ", "a", " ", "k"]], "+", RowBox[List["a", " ", "m"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]], ")"]]]]]], "]"]]]]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z n b z 2 + d z + e sin m ( a z 2 + p z + q ) cos v ( c z 2 + f z + g ) z 2 - m - v - 1 b - n - 1 - d 2 4 b ( b n + 1 d 2 4 b ( ( 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 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( d + ( m - 2 k ) p ) 2 4 ( b + a ( 2 k - m ) ) + e + ( 2 k - m ) q + m π 2 ( j = 0 n 2 j - n ( - d - 2 k p + m p ) n - j ( d + ( 2 k - m ) p + 2 ( b + a ( 2 k - m ) ) z ) j + 1 ( - ( d + ( 2 k - m ) p + 2 ( b + a ( 2 k - m ) ) z ) 2 b + a ( 2 k - m ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( 2 k - m ) p + 2 ( b + a ( 2 k - m ) ) z ) 2 4 ( b + a ( 2 k - m ) ) ) ) ( b + a ( 2 k - m ) ) - n - 1 + - ( d + ( m - 2 k ) p ) 2 4 ( b + a ( m - 2 k ) ) + e + ( m - 2 k ) q - m π 2 ( b + a ( m - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - d - ( m - 2 k ) p ) n - j ( d + ( m - 2 k ) p + 2 ( b + a ( m - 2 k ) ) z ) j + 1 ( - ( d + ( m - 2 k ) p + 2 ( b + a ( m - 2 k ) ) z ) 2 b + a ( m - 2 k ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( m - 2 k ) p + 2 ( b + a ( m - 2 k ) ) z ) 2 4 ( b + a ( m - 2 k ) ) ) ) + ( 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]]]]] ( ( d - 2 f s + f v ) 2 4 ( b + 2 c s - c v ) + e + g ( 2 s - v ) ( j = 0 n 2 j - n ( - d - 2 f s + f v ) n - j ( d + f ( 2 s - v ) + 2 ( b + 2 c s - c v ) z ) j + 1 ( - ( d + f ( 2 s - v ) + 2 ( b + 2 c s - c v ) z ) 2 b + 2 c s - c v ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + f ( 2 s - v ) + 2 ( b + 2 c s - c v ) z ) 2 4 ( b + 2 c s - c v ) ) ) ( b + 2 c s - c v ) - n - 1 + - ( d + f ( v - 2 s ) ) 2 4 ( b + c ( v - 2 s ) ) + e + g ( v - 2 s ) ( b + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d - f ( v - 2 s ) ) n - j ( d + f ( v - 2 s ) + 2 ( b + c ( v - 2 s ) ) z ) j + 1 ( - ( d + f ( v - 2 s ) + 2 ( b + c ( v - 2 s ) ) z ) 2 b + c ( v - 2 s ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + f ( v - 2 s ) + 2 ( b + c ( v - 2 s ) ) z ) 2 4 ( b + c ( v - 2 s ) ) ) ) - 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 + m π + 4 k q - 2 m q + 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]]]]] ( - ( d + ( m - 2 k ) p + f ( v - 2 s ) ) 2 4 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) ( j = 0 n 2 j - n ( ( 2 k p - m p + 2 f s - f v ) - d ) n - j ( d + ( m - 2 k ) p + f ( v - 2 s ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) z ) j + 1 ( - ( d + ( m - 2 k ) p + f ( v - 2 s ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) z ) 2 / ( b + a ( m - 2 k ) + c ( v - 2 s ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + ( m - 2 k ) p + f ( v - 2 s ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) z ) 2 / ( 4 ( b + a ( m - 2 k ) + c ( v - 2 s ) ) ) ) ) ( b + a ( m - 2 k ) + c ( v - 2 s ) ) - n - 1 + ( - 2 q m + π m + 4 k q ) ( - ( d - 2 k p + m p + 2 f s - f v ) 2 4 ( - b + 2 a k - a m - 2 c s + c v ) ( j = 0 n 2 j - n ( ( - 2 k p + m p + 2 f s - f v ) - d ) n - j ( ( d + m p + 2 f s - f v + 2 b z + 2 a m z + 4 c s z - 2 c v z - 2 k ( p + 2 a z ) ) 2 / ( b + ( 2 a k - a m - 2 c s + c v ) ) ) 1 2 ( - j - 1 ) ( d + ( - 2 f s - 4 c z s + f v - 2 b z + 2 c v z + 2 k ( p + 2 a z ) - m ( p + 2 a z ) ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( ( d + m p + 2 f s - f v + 2 b z + 2 a m z + 4 c s z - 2 c v z - 2 k ( p + 2 a z ) ) 2 ) / ( 4 ( - b + 2 a k - a m - 2 c s + c v ) ) ) ) ( b + ( 2 a k - a m - 2 c s + c v ) ) - n - 1 + 1 4 ( ( d - 2 k p + m p - 2 f s + f v ) 2 b - 2 a k + a m - 2 c s + c v + 8 g ( 2 s - v ) ) ( b + ( 2 a k - a m + 2 c s - c v ) ) - n - 1 j = 0 n 2 j - n ( - d - ( 2 k p - m p + 2 f s - f v ) ) n - j ( ( d + m p - 2 f s + f v + 2 b z + 2 a m z - 4 c s z + 2 c v z - 2 k ( p + 2 a z ) ) 2 / ( b + ( 2 a k - a m + 2 c s - c v ) ) ) 1 2 ( - j - 1 ) ( d + ( 2 f s + 4 c z s - f v - 2 b z - 2 c v z + 2 k ( p + 2 a z ) - m ( p + 2 a z ) ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( ( d + m p - 2 f s + f v + 2 b z + 2 a m z - 4 c s z + 2 c v z - 2 k ( p + 2 a z ) ) 2 ) / ( 4 ( b - 2 a k + a m - 2 c s + c v ) ) ) ) + 1 4 ( ( d + 2 k p - m p - 2 f s + f v ) 2 b + 2 a k - a m - 2 c s + c v + 8 g ( 2 s - v ) ) ( b - ( 2 a k - a m - 2 c s + c v ) ) - n - 1 j = 0 n 2 j - n ( ( 2 k p - m p - 2 f s + f v ) - d ) n - j ( ( d + 2 k p - m p - 2 f s + f v + 2 b z + 4 a k z - 2 a m z - 4 c s z + 2 c v z ) 2 / ( b - ( 2 a k - a m - 2 c s + c v ) ) ) 1 2 ( - j - 1 ) ( d - ( - 2 f s - 4 c z s + f v + 2 b z + 2 c v z + 2 k ( p + 2 a z ) - m ( p + 2 a z ) ) ) j + 1 ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( ( d + 2 k p - m p - 2 f s + f v + 2 b z + 4 a k z - 2 a m z - 4 c s z + 2 c v z ) 2 ) / ( 4 ( b + 2 a k - a m - 2 c s + c v ) ) ) ) ) - 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]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) ( v mod 2 \$CellContext`v 2 - 1 ) j = 0 n 2 j - n ( - d ) n - j ( d + 2 b z ) j + 1 ( - ( d + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + 2 b z ) 2 4 b ) ) /; n m + v + Condition z z n b z 2 d z e a z 2 p z q m c z 2 f z g v 2 -1 m -1 v -1 b -1 n -1 -1 d 2 4 b -1 b n 1 d 2 4 b -1 Binomial v v 2 -1 \$CellContext`v 2 -1 k 0 m -1 2 -1 -1 k Binomial m k d m -1 2 k p 2 4 b a 2 k -1 m -1 e 2 k -1 m q m 2 -1 j 0 n 2 j -1 n -1 d -1 2 k p m p n -1 j d 2 k -1 m p 2 b a 2 k -1 m z j 1 -1 d 2 k -1 m p 2 b a 2 k -1 m z 2 b a 2 k -1 m -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 k -1 m p 2 b a 2 k -1 m z 2 4 b a 2 k -1 m -1 b a 2 k -1 m -1 n -1 -1 d m -1 2 k p 2 4 b a m -1 2 k -1 e m -1 2 k q -1 m 2 -1 b a m -1 2 k -1 n -1 j 0 n 2 j -1 n -1 d -1 m -1 2 k p n -1 j d m -1 2 k p 2 b a m -1 2 k z j 1 -1 d m -1 2 k p 2 b a m -1 2 k z 2 b a m -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k p 2 b a m -1 2 k z 2 4 b a m -1 2 k -1 Binomial m m 2 -1 \$CellContext`m 2 -1 s 0 v -1 2 -1 Binomial v s d -1 2 f s f v 2 4 b 2 c s -1 c v -1 e g 2 s -1 v j 0 n 2 j -1 n -1 d -1 2 f s f v n -1 j d f 2 s -1 v 2 b 2 c s -1 c v z j 1 -1 d f 2 s -1 v 2 b 2 c s -1 c v z 2 b 2 c s -1 c v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f 2 s -1 v 2 b 2 c s -1 c v z 2 4 b 2 c s -1 c v -1 b 2 c s -1 c v -1 n -1 -1 d f v -1 2 s 2 4 b c v -1 2 s -1 e g v -1 2 s b c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d -1 f v -1 2 s n -1 j d f v -1 2 s 2 b c v -1 2 s z j 1 -1 d f v -1 2 s 2 b c v -1 2 s z 2 b c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f v -1 2 s 2 b c v -1 2 s z 2 4 b c v -1 2 s -1 -1 k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 -1 1 2 2 e m 4 k q -1 2 m q 4 g s -1 2 g v Binomial v s -1 d m -1 2 k p f v -1 2 s 2 4 b a m -1 2 k c v -1 2 s -1 j 0 n 2 j -1 n 2 k p -1 m p 2 f s -1 f v -1 d n -1 j d m -1 2 k p f v -1 2 s 2 b a m -1 2 k c v -1 2 s z j 1 -1 d m -1 2 k p f v -1 2 s 2 b a m -1 2 k c v -1 2 s z 2 b a m -1 2 k c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k p f v -1 2 s 2 b a m -1 2 k c v -1 2 s z 2 4 b a m -1 2 k c v -1 2 s -1 b a m -1 2 k c v -1 2 s -1 n -1 -2 q m m 4 k q -1 d -1 2 k p m p 2 f s -1 f v 2 4 -1 b 2 a k -1 a m -1 2 c s c v -1 j 0 n 2 j -1 n -2 k p m p 2 f s -1 f v -1 d n -1 j d m p 2 f s -1 f v 2 b z 2 a m z 4 c s z -1 2 c v z -1 2 k p 2 a z 2 b 2 a k -1 a m -1 2 c s c v -1 1 2 -1 j -1 d -2 f s -1 4 c z s f v -1 2 b z 2 c v z 2 k p 2 a z -1 m p 2 a z j 1 Binomial n j Gamma j 1 2 -1 -1 d m p 2 f s -1 f v 2 b z 2 a m z 4 c s z -1 2 c v z -1 2 k p 2 a z 2 4 -1 b 2 a k -1 a m -1 2 c s c v -1 b 2 a k -1 a m -1 2 c s c v -1 n -1 1 4 d -1 2 k p m p -1 2 f s f v 2 b -1 2 a k a m -1 2 c s c v -1 8 g 2 s -1 v b 2 a k -1 a m 2 c s -1 c v -1 n -1 j 0 n 2 j -1 n -1 d -1 2 k p -1 m p 2 f s -1 f v n -1 j d m p -1 2 f s f v 2 b z 2 a m z -1 4 c s z 2 c v z -1 2 k p 2 a z 2 b 2 a k -1 a m 2 c s -1 c v -1 1 2 -1 j -1 d 2 f s 4 c z s -1 f v -1 2 b z -1 2 c v z 2 k p 2 a z -1 m p 2 a z j 1 Binomial n j Gamma j 1 2 -1 d m p -1 2 f s f v 2 b z 2 a m z -1 4 c s z 2 c v z -1 2 k p 2 a z 2 4 b -1 2 a k a m -1 2 c s c v -1 1 4 d 2 k p -1 m p -1 2 f s f v 2 b 2 a k -1 a m -1 2 c s c v -1 8 g 2 s -1 v b -1 2 a k -1 a m -1 2 c s c v -1 n -1 j 0 n 2 j -1 n 2 k p -1 m p -1 2 f s f v -1 d n -1 j d 2 k p -1 m p -1 2 f s f v 2 b z 4 a k z -1 2 a m z -1 4 c s z 2 c v z 2 b -1 2 a k -1 a m -1 2 c s c v -1 1 2 -1 j -1 d -1 -2 f s -1 4 c z s f v 2 b z 2 c v z 2 k p 2 a z -1 m p 2 a z j 1 Binomial n j Gamma j 1 2 -1 d 2 k p -1 m p -1 2 f s f v 2 b z 4 a k z -1 2 a m z -1 4 c s z 2 c v z 2 4 b 2 a k -1 a m -1 2 c s c v -1 -1 e Binomial m m 2 -1 Binomial v v 2 -1 \$CellContext`m 2 -1 \$CellContext`v 2 -1 j 0 n 2 j -1 n -1 d n -1 j d 2 b z j 1 -1 d 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 b z 2 4 b -1 n m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18