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 Cos

 http://functions.wolfram.com/01.07.21.2556.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18