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 Cosh

 http://functions.wolfram.com/01.20.21.3945.01

 Input Form

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

 Rule Form

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

 2002-12-18