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 Cosh

 http://functions.wolfram.com/01.20.21.3949.01

 Input Form

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

 Standard Form

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RowBox[List["m", "-", RowBox[List["2", " ", "u"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18