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 Cosh

 http://functions.wolfram.com/01.20.21.4011.01

 Input Form

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

 Rule Form

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

 2002-12-18