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/01.07.21.2752.01

 Input Form

 Integrate[z^n E^(p Sqrt[z]) Sin[b Sqrt[z]]^m Cos[c z]^v, z] == 2^(-1 - m - v) ((-4 Binomial[m, m/2] Binomial[v, v/2] Gamma[2 (1 + n), (-p) Sqrt[z]] (-1 + Mod[m, 2]) (-1 + Mod[v, 2]))/ p^(2 (1 + n)) + (4 z^(1 + n) Binomial[v, v/2] (-1 + Mod[v, 2]) Sum[(-1)^u Binomial[m, u] (((-1)^m Gamma[2 (1 + n), (-(p - I b (m - 2 u))) Sqrt[z]])/ ((-(p - I b (m - 2 u))) Sqrt[z])^(2 (1 + n)) + Gamma[2 (1 + n), (-(p + I b (m - 2 u))) Sqrt[z]]/ ((-(p + I b (m - 2 u))) Sqrt[z])^(2 (1 + n))), {u, 0, Floor[(1/2) (-1 + m)]}])/I^m - 4 Binomial[m, m/2] (-1 + Mod[m, 2]) Sum[(-2^(-2 (1 + n))) E^((I p^2)/(-8 c s + 4 c v)) (c^2 (-2 s + v)^2)^(-1 - 2 n) Binomial[v, s] (E^((I p^2)/(4 c s - 2 c v)) (I c (-2 s + v))^(2 n) Sum[(-1)^(-h + k) 4^k p^(-h - k + 2 n) (p + 2 I c (2 s - v) Sqrt[z])^ (h + k) ((I (p + 2 I c (2 s - v) Sqrt[z])^2)/(c (2 s - v)))^ ((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] (p (p + 2 I c (2 s - v) Sqrt[z]) Gamma[(1/2) (1 + h + k), (I (p + 2 I c (2 s - v) Sqrt[z])^2)/(c (8 s - 4 v))] + 2 I c (2 s - v) Sqrt[(I (p + 2 I c (2 s - v) Sqrt[z])^2)/(c (2 s - v))] Gamma[(1/2) (2 + h + k), (I (p + 2 I c (2 s - v) Sqrt[z])^2)/(c (8 s - 4 v))]), {k, 0, n}, {h, 0, k}] + (I c (2 s - v))^(2 n) Sum[(-1)^(-h + k) 4^k p^(-h - k + 2 n) (p + 2 I c (-2 s + v) Sqrt[z])^(h + k) ((I (p + 2 I c (-2 s + v) Sqrt[z])^2)/(c (-2 s + v)))^ ((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] (p (p + 2 I c (-2 s + v) Sqrt[z]) Gamma[(1/2) (1 + h + k), -((I (p + 2 I c (-2 s + v) Sqrt[z])^2)/(c (8 s - 4 v)))] + 2 I c (-2 s + v) Sqrt[-((I (p + 2 I c (-2 s + v) Sqrt[z])^2)/ (c (2 s - v)))] Gamma[(1/2) (2 + h + k), -((I (p + 2 I c (-2 s + v) Sqrt[z])^2)/(c (8 s - 4 v)))]), {k, 0, n}, {h, 0, k}]), {s, 0, Floor[(1/2) (-1 + v)]}] - (1/c^2) (Sum[(1/(-2 s + v)^2) (Binomial[v, s] Sum[(-1)^u Binomial[m, u] ((E^((I (p + I b (m - 2 u))^2)/ (c (8 s - 4 v))) Sum[(-1)^(-h + k) 4^k (p + I b (m - 2 u))^ (-h - k + 2 n) (p + I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z])^ (h + k) ((I (p + I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z])^2)/ (c (2 s - v)))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((p + I b (m - 2 u)) (p + I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z]) Gamma[(1/2) (1 + h + k), (I (p + I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z])^2)/ (c (8 s - 4 v))] + 2 I c (2 s - v) Sqrt[ (I (p + I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z])^2)/ (c (2 s - v))] Gamma[(1/2) (2 + h + k), (I (p + I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z])^2)/ (c (8 s - 4 v))]), {k, 0, n}, {h, 0, k}])/ (I c (2 s - v))^(2 n) + (E^((1/4) I (4 m Pi + (b m + I p - 2 b u)^2/(2 c s - c v))) Sum[(-1)^(-h + k) 4^k (p - I b (m - 2 u))^(-h - k + 2 n) (p - I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z])^(h + k) ((I (p - I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z])^2)/ (c (-2 s + v)))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((p - I b (m - 2 u)) (p - I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z]) Gamma[(1/2) (1 + h + k), (I (I p + b (m - 2 u) + 2 c (2 s - v) Sqrt[z])^2)/ (c (8 s - 4 v))] + 2 I c (-2 s + v) Sqrt[ (I (p - I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z])^2)/ (c (-2 s + v))] Gamma[(1/2) (2 + h + k), (I (I p + b (m - 2 u) + 2 c (2 s - v) Sqrt[z])^2)/ (c (8 s - 4 v))]), {k, 0, n}, {h, 0, k}] + E^((I b m + p - 2 I b u)^2/(8 I c s - 4 I c v)) Sum[ (-1)^(-h + k) 4^k (p + I b (m - 2 u))^(-h - k + 2 n) (p + I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z])^(h + k) ((I (p + I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z])^2)/ (c (-2 s + v)))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((p + I b (m - 2 u)) (p + I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z]) Gamma[(1/2) (1 + h + k), (I ((-I) p + b (m - 2 u) + 2 c (-2 s + v) Sqrt[z])^2)/ (c (8 s - 4 v))] + 2 I c (-2 s + v) Sqrt[ (I (p + I b (m - 2 u) + 2 I c (-2 s + v) Sqrt[z])^2)/ (c (-2 s + v))] Gamma[(1/2) (2 + h + k), (I ((-I) p + b (m - 2 u) + 2 c (-2 s + v) Sqrt[z])^2)/ (c (8 s - 4 v))]), {k, 0, n}, {h, 0, k}])/ (I c (-2 s + v))^(2 n) + (E^(I (m Pi + (p - I b (m - 2 u))^2/ (c (8 s - 4 v)))) Sum[(-1)^(-h + k) 4^k (p - I b (m - 2 u))^ (-h - k + 2 n) (p - I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z])^ (h + k) (-((I (I p + b (m - 2 u) + 2 c (-2 s + v) Sqrt[z])^ 2)/(c (2 s - v))))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((p - I b (m - 2 u)) (p - I b (m - 2 u) + 2 I c (2 s - v) Sqrt[z]) Gamma[(1/2) (1 + h + k), -((I (I p + b (m - 2 u) + 2 c (-2 s + v) Sqrt[z])^2)/ (c (8 s - 4 v)))] + 2 I c (2 s - v) Sqrt[ -((I (I p + b (m - 2 u) + 2 c (-2 s + v) Sqrt[z])^2)/ (c (2 s - v)))] Gamma[(1/2) (2 + h + k), -((I (I p + b (m - 2 u) + 2 c (-2 s + v) Sqrt[z])^2)/ (c (8 s - 4 v)))]), {k, 0, n}, {h, 0, k}])/ (I c (2 s - v))^(2 n)), {u, 0, Floor[(1/2) (-1 + m)]}]), {s, 0, Floor[(1/2) (-1 + v)]}]/(I^m 4^n))) /; 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 - 1 ( - 4 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]]]]] ( 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 ( 2 ( n + 1 ) , - p z ) ( m mod 2 \$CellContext`m 2 - 1 ) ( v mod 2 \$CellContext`v 2 - 1 ) + 4 - m z n + 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]]]]] ( v mod 2 \$CellContext`v 2 - 1 ) u = 0 m - 1 2 ( - 1 ) u ( m u ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["u", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( Γ ( 2 ( n + 1 ) , - ( p + b ( m - 2 u ) ) z ) ( - ( p + b ( m - 2 u ) ) z ) - 2 ( n + 1 ) + ( - 1 ) m ( - ( p - b ( m - 2 u ) ) z ) - 2 ( n + 1 ) Γ ( 2 ( n + 1 ) , - ( p - b ( m - 2 u ) ) z ) ) - 4 ( 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 - 2 - 2 ( n + 1 ) p 2 4 c v - 8 c s ( c 2 ( v - 2 s ) 2 ) - 2 n - 1 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( k = 0 n h = 0 k ( - 1 ) k - h 4 k p - h - k + 2 n ( p + 2 c ( v - 2 s ) z ) h + k ( ( p + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( p ( p + 2 c ( v - 2 s ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( p + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) + 2 c - ( p + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) ( v - 2 s ) Γ ( 1 2 ( h + k + 2 ) , - ( p + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) ) ) ( c ( 2 s - v ) ) 2 n + p 2 4 c s - 2 c v ( c ( v - 2 s ) ) 2 n k = 0 n h = 0 k ( - 1 ) k - h 4 k p - h - k + 2 n ( p + 2 c ( 2 s - v ) z ) h + k ( ( p + 2 c ( 2 s - v ) z ) 2 c ( 2 s - v ) ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( p ( p + 2 c ( 2 s - v ) z ) Γ ( 1 2 ( h + k + 1 ) , ( p + 2 c ( 2 s - v ) z ) 2 c ( 8 s - 4 v ) ) + 2 c ( 2 s - v ) ( p + 2 c ( 2 s - v ) z ) 2 c ( 2 s - v ) Γ ( 1 2 ( h + k + 2 ) , ( p + 2 c ( 2 s - v ) z ) 2 c ( 8 s - 4 v ) ) ) ) - 1 c 2 ( - m 4 - n s = 0 v - 1 2 1 ( v - 2 s ) 2 ( ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] u = 0 m - 1 2 ( - 1 ) u ( m u ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["u", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p + b ( m - 2 u ) ) 2 c ( 8 s - 4 v ) ( k = 0 n h = 0 k ( - 1 ) k - h 4 k ( p + b ( m - 2 u ) ) - h - k + 2 n ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) h + k ( ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) 2 c ( 2 s - v ) ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p + b ( m - 2 u ) ) ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) Γ ( 1 2 ( h + k + 1 ) , ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) 2 c ( 8 s - 4 v ) ) + 2 c ( 2 s - v ) ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) 2 c ( 2 s - v ) Γ ( 1 2 ( h + k + 2 ) , ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) 2 c ( 8 s - 4 v ) ) ) ) ( c ( 2 s - v ) ) - 2 n + ( ( p - b ( m - 2 u ) ) 2 c ( 8 s - 4 v ) + m π ) ( k = 0 n h = 0 k ( - 1 ) k - h 4 k ( p - b ( m - 2 u ) ) - h - k + 2 n ( p - b ( m - 2 u ) + 2 c ( 2 s - v ) z ) h + k ( - ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p - b ( m - 2 u ) ) ( p - b ( m - 2 u ) + 2 c ( 2 s - v ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) + 2 c ( 2 s - v ) - ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( 2 s - v ) Γ ( 1 2 ( h + k + 2 ) , - ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) ) ) ( c ( 2 s - v ) ) - 2 n + ( c ( v - 2 s ) ) - 2 n ( 1 4 ( ( b m + p - 2 b u ) 2 2 c s - c v + 4 m π ) k = 0 n h = 0 k ( - 1 ) k - h 4 k ( p - b ( m - 2 u ) ) - h - k + 2 n ( p - b ( m - 2 u ) + 2 c ( v - 2 s ) z ) h + k ( ( p - b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p - b ( m - 2 u ) ) ( p - b ( m - 2 u ) + 2 c ( v - 2 s ) z ) Γ ( 1 2 ( h + k + 1 ) , ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) 2 c ( 8 s - 4 v ) ) + 2 c ( v - 2 s ) Γ ( 1 2 ( h + k + 2 ) , ( p + b ( m - 2 u ) + 2 c ( 2 s - v ) z ) 2 c ( 8 s - 4 v ) ) ( p - b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) + ( b m + p - 2 b u ) 2 8 c s - 4 c v k = 0 n h = 0 k ( - 1 ) k - h 4 k ( p + b ( m - 2 u ) ) - h - k + 2 n ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) h + k ( ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) 1 2 ( - h - k - 1 ) ( k h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p + b ( m - 2 u ) ) ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) Γ ( 1 2 ( h + k + 1 ) , ( - p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) + 2 c ( v - 2 s ) Γ ( 1 2 ( h + k + 2 ) , ( - p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( 8 s - 4 v ) ) ( p + b ( m - 2 u ) + 2 c ( v - 2 s ) z ) 2 c ( v - 2 s ) ) ) ) ) ) ) /; m + v + n Condition z z n p z 1 2 b z 1 2 m c z v 2 -1 m -1 v -1 -4 p -2 n 1 Binomial m m 2 -1 Binomial v v 2 -1 Gamma 2 n 1 -1 p z 1 2 \$CellContext`m 2 -1 \$CellContext`v 2 -1 4 -1 m z n 1 Binomial v v 2 -1 \$CellContext`v 2 -1 u 0 m -1 2 -1 -1 u Binomial m u Gamma 2 n 1 -1 p b m -1 2 u z 1 2 -1 p b m -1 2 u z 1 2 -2 n 1 -1 m -1 p -1 b m -1 2 u z 1 2 -2 n 1 Gamma 2 n 1 -1 p -1 b m -1 2 u z 1 2 -1 4 Binomial m m 2 -1 \$CellContext`m 2 -1 s 0 v -1 2 -1 -1 2 -2 n 1 p 2 4 c v -1 8 c s -1 c 2 v -1 2 s 2 -2 n -1 Binomial v s h 0 k k 0 n -1 k -1 h 4 k p -1 h -1 k 2 n p 2 c v -1 2 s z 1 2 h k p 2 c v -1 2 s z 1 2 2 c v -1 2 s -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k p p 2 c v -1 2 s z 1 2 Gamma 1 2 h k 1 -1 p 2 c v -1 2 s z 1 2 2 c 8 s -1 4 v -1 2 c -1 p 2 c v -1 2 s z 1 2 2 c 2 s -1 v -1 1 2 v -1 2 s Gamma 1 2 h k 2 -1 p 2 c v -1 2 s z 1 2 2 c 8 s -1 4 v -1 c 2 s -1 v 2 n p 2 4 c s -1 2 c v -1 c v -1 2 s 2 n h 0 k k 0 n -1 k -1 h 4 k p -1 h -1 k 2 n p 2 c 2 s -1 v z 1 2 h k p 2 c 2 s -1 v z 1 2 2 c 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k p p 2 c 2 s -1 v z 1 2 Gamma 1 2 h k 1 p 2 c 2 s -1 v z 1 2 2 c 8 s -1 4 v -1 2 c 2 s -1 v p 2 c 2 s -1 v z 1 2 2 c 2 s -1 v -1 1 2 Gamma 1 2 h k 2 p 2 c 2 s -1 v z 1 2 2 c 8 s -1 4 v -1 -1 1 c 2 -1 -1 m 4 -1 n s 0 v -1 2 -1 1 v -1 2 s 2 -1 Binomial v s u 0 m -1 2 -1 -1 u Binomial m u p b m -1 2 u 2 c 8 s -1 4 v -1 h 0 k k 0 n -1 k -1 h 4 k p b m -1 2 u -1 h -1 k 2 n p b m -1 2 u 2 c 2 s -1 v z 1 2 h k p b m -1 2 u 2 c 2 s -1 v z 1 2 2 c 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k p b m -1 2 u p b m -1 2 u 2 c 2 s -1 v z 1 2 Gamma 1 2 h k 1 p b m -1 2 u 2 c 2 s -1 v z 1 2 2 c 8 s -1 4 v -1 2 c 2 s -1 v p b m -1 2 u 2 c 2 s -1 v z 1 2 2 c 2 s -1 v -1 1 2 Gamma 1 2 h k 2 p b m -1 2 u 2 c 2 s -1 v z 1 2 2 c 8 s -1 4 v -1 c 2 s -1 v -2 n p -1 b m -1 2 u 2 c 8 s -1 4 v -1 m h 0 k k 0 n -1 k -1 h 4 k p -1 b m -1 2 u -1 h -1 k 2 n p -1 b m -1 2 u 2 c 2 s -1 v z 1 2 h k -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k p -1 b m -1 2 u p -1 b m -1 2 u 2 c 2 s -1 v z 1 2 Gamma 1 2 h k 1 -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c 8 s -1 4 v -1 2 c 2 s -1 v -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c 2 s -1 v -1 1 2 Gamma 1 2 h k 2 -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c 8 s -1 4 v -1 c 2 s -1 v -2 n c v -1 2 s -2 n 1 4 b m p -1 2 b u 2 2 c s -1 c v -1 4 m h 0 k k 0 n -1 k -1 h 4 k p -1 b m -1 2 u -1 h -1 k 2 n p -1 b m -1 2 u 2 c v -1 2 s z 1 2 h k p -1 b m -1 2 u 2 c v -1 2 s z 1 2 2 c v -1 2 s -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k p -1 b m -1 2 u p -1 b m -1 2 u 2 c v -1 2 s z 1 2 Gamma 1 2 h k 1 p b m -1 2 u 2 c 2 s -1 v z 1 2 2 c 8 s -1 4 v -1 2 c v -1 2 s Gamma 1 2 h k 2 p b m -1 2 u 2 c 2 s -1 v z 1 2 2 c 8 s -1 4 v -1 p -1 b m -1 2 u 2 c v -1 2 s z 1 2 2 c v -1 2 s -1 1 2 b m p -1 2 b u 2 8 c s -1 4 c v -1 h 0 k k 0 n -1 k -1 h 4 k p b m -1 2 u -1 h -1 k 2 n p b m -1 2 u 2 c v -1 2 s z 1 2 h k p b m -1 2 u 2 c v -1 2 s z 1 2 2 c v -1 2 s -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k p b m -1 2 u p b m -1 2 u 2 c v -1 2 s z 1 2 Gamma 1 2 h k 1 -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c 8 s -1 4 v -1 2 c v -1 2 s Gamma 1 2 h k 2 -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c 8 s -1 4 v -1 p b m -1 2 u 2 c v -1 2 s z 1 2 2 c v -1 2 s -1 1 2 m SuperPlus v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18