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/01.07.21.2760.01

 Input Form

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

 Rule Form

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

 2002-12-18