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 Cosh

 http://functions.wolfram.com/01.20.21.4005.01

 Input Form

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