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/01.07.21.2738.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18