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/01.07.21.2758.01

 Input Form

 Integrate[z^n E^(p z) Sin[b z]^m Cos[c Sqrt[z]]^v, z] == (-2^(-m - v)) (-p)^(-1 - n) Binomial[m, m/2] Binomial[v, v/2] Gamma[1 + n, (-p) z] (1 - Mod[m, 2]) (1 - Mod[v, 2]) - 2^(-m - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] ((((-I) b (-2 k + m) - p)^(-1 - n) Gamma[1 + n, ((-I) b (-2 k + m) - p) z])/E^((1/2) I m Pi) + E^((I m Pi)/2) (I b (-2 k + m) - p)^(-1 - n) Gamma[1 + n, (I b (-2 k + m) - p) z]), {k, 0, Floor[(1/2) (-1 + m)]}] + (2^(-m - v - 2 n - 1) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, s] (E^((c^2 (-2 s + v)^2)/(4 p)) Sum[(-1)^(-h + i) 4^i ((-I) c (-2 s + v))^(-h - i + 2 n) ((-I) c (-2 s + v) + 2 p Sqrt[z])^(h + i) (-(((-I) c (-2 s + v) + 2 p Sqrt[z])^2/p))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((-I) c (-2 s + v) ((-I) c (-2 s + v) + 2 p Sqrt[z]) Gamma[(1/2) (1 + h + i), -(((-I) c (-2 s + v) + 2 p Sqrt[z])^2/(4 p))] + 2 p Sqrt[-(((-I) c (-2 s + v) + 2 p Sqrt[z])^2/p)] Gamma[(1/2) (2 + h + i), -(((-I) c (-2 s + v) + 2 p Sqrt[z])^2/ (4 p))]), {i, 0, n}, {h, 0, i}] + E^((c^2 (-2 s + v)^2)/(4 p)) Sum[(-1)^(-h + i) 4^i (I c (-2 s + v))^(-h - i + 2 n) (I c (-2 s + v) + 2 p Sqrt[z])^ (h + i) (-((I c (-2 s + v) + 2 p Sqrt[z])^2/p))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] (I c (-2 s + v) (I c (-2 s + v) + 2 p Sqrt[z]) Gamma[(1/2) (1 + h + i), -((I c (-2 s + v) + 2 p Sqrt[z])^2/ (4 p))] + 2 p Sqrt[-((I c (-2 s + v) + 2 p Sqrt[z])^2/p)] Gamma[(1/2) (2 + h + i), -((I c (-2 s + v) + 2 p Sqrt[z])^2/ (4 p))]), {i, 0, n}, {h, 0, i}]), {s, 0, Floor[(1/2) (-1 + v)]}])/p^(2 (1 + n)) + 2^(-m - v - 2 n - 1) Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, s] ((E^((I m Pi)/2 + (c^2 (-2 s + v)^2)/ (4 ((-I) b (-2 k + m) + p))) Sum[(-1)^(-h + i) 4^i ((-I) c (-2 s + v))^(-h - i + 2 n) ((-I) c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^(h + i) (-(((-I) c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/ ((-I) b (-2 k + m) + p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((-I) c (-2 s + v) ((-I) c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -(((-I) c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/ (4 ((-I) b (-2 k + m) + p)))] + 2 ((-I) b (-2 k + m) + p) Sqrt[-(((-I) c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/((-I) b (-2 k + m) + p))] Gamma[ (1/2) (2 + h + i), -(((-I) c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/(4 ((-I) b (-2 k + m) + p)))]), {i, 0, n}, {h, 0, i}])/((-I) b (-2 k + m) + p)^(2 (1 + n)) + (E^((I m Pi)/2 + (c^2 (-2 s + v)^2)/(4 ((-I) b (-2 k + m) + p))) Sum[(-1)^(-h + i) 4^i (I c (-2 s + v))^(-h - i + 2 n) (I c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^(h + i) (-((I c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/ ((-I) b (-2 k + m) + p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] (I c (-2 s + v) (I c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((I c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/ (4 ((-I) b (-2 k + m) + p)))] + 2 ((-I) b (-2 k + m) + p) Sqrt[-((I c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/((-I) b (-2 k + m) + p))] Gamma[ (1/2) (2 + h + i), -((I c (-2 s + v) + 2 ((-I) b (-2 k + m) + p) Sqrt[z])^2/(4 ((-I) b (-2 k + m) + p)))]), {i, 0, n}, {h, 0, i}])/((-I) b (-2 k + m) + p)^(2 (1 + n)) + (E^((-(1/2)) I m Pi + (c^2 (-2 s + v)^2)/(4 (I b (-2 k + m) + p))) Sum[(-1)^(-h + i) 4^i ((-I) c (-2 s + v))^(-h - i + 2 n) ((-I) c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^(h + i) (-(((-I) c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (I b (-2 k + m) + p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((-I) c (-2 s + v) ((-I) c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -(((-I) c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (4 (I b (-2 k + m) + p)))] + 2 (I b (-2 k + m) + p) Sqrt[ -(((-I) c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (I b (-2 k + m) + p))] Gamma[(1/2) (2 + h + i), -(((-I) c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (4 (I b (-2 k + m) + p)))]), {i, 0, n}, {h, 0, i}])/ (I b (-2 k + m) + p)^(2 (1 + n)) + (E^((-(1/2)) I m Pi + (c^2 (-2 s + v)^2)/(4 (I b (-2 k + m) + p))) Sum[(-1)^(-h + i) 4^i (I c (-2 s + v))^(-h - i + 2 n) (I c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^(h + i) (-((I c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (I b (-2 k + m) + p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] (I c (-2 s + v) (I c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((I c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (4 (I b (-2 k + m) + p)))] + 2 (I b (-2 k + m) + p) Sqrt[ -((I c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (I b (-2 k + m) + p))] Gamma[(1/2) (2 + h + i), -((I c (-2 s + v) + 2 (I b (-2 k + m) + p) Sqrt[z])^2/ (4 (I b (-2 k + m) + p)))]), {i, 0, n}, {h, 0, i}])/ (I b (-2 k + m) + p)^(2 (1 + n))), {s, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0 && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18