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 Cosh

 http://functions.wolfram.com/01.20.21.4009.01

 Input Form

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

 Rule Form

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

 2002-12-18