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 Cosh

 http://functions.wolfram.com/01.20.21.4594.01

 Input Form

 Integrate[z^n Sinh[b Sqrt[z] + e]^m Cosh[c Sqrt[z] + f z + g]^v, z] == 2^(-1 - m - v) ((1/(1 + n)) ((2 z^(1 + n) Binomial[m, m/2] Binomial[v, v/2] (-1 + Mod[m, 2]) (-1 + Mod[v, 2]))/I^m) - (4 Binomial[v, v/2] (1 - Mod[v, 2]) Sum[((-1)^k E^(-2 e k - e m) Binomial[m, k] ((-1)^m E^(4 e k) Gamma[2 (1 + n), (-b) (2 k - m) Sqrt[z]] + E^(2 e m) Gamma[2 (1 + n), b (2 k - m) Sqrt[z]]))/ (-2 k + m)^(2 (1 + n)), {k, 0, Floor[(1/2) (-1 + m)]}])/ b^(2 (1 + n)) - (1/c) ((Binomial[m, m/2] (-1 + Mod[m, 2]) Sum[((-2 s + v)^(-2 - 2 n) Binomial[v, s] (Sum[(-1)^(-h + k) 4^k c (2 s - v) (c (-2 s + v))^(-h - k + 2 n) ((-(2 s - v)) (c + 2 f Sqrt[z]))^(h + k) (((2 s - v) (c + 2 f Sqrt[z])^2)/f)^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] (c (2 s - v) (c + 2 f Sqrt[z]) Gamma[(1/2) (1 + h + k), ((2 s - v) (c + 2 f Sqrt[z])^2)/ (4 f)] - 2 f Sqrt[((2 s - v) (c + 2 f Sqrt[z])^2)/f] Gamma[ (1/2) (2 + h + k), ((2 s - v) (c + 2 f Sqrt[z])^2)/(4 f)]), {k, 0, n}, {h, 0, k}] + E^(((-c^2 + 4 f g) (2 s - v))/(2 f)) Sum[(-1)^(-h + k) 4^k (c (2 s - v))^(1 - h - k + 2 n) ((2 s - v) (c + 2 f Sqrt[z]))^(h + k) (-(((2 s - v) (c + 2 f Sqrt[z])^2)/f))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] (c (2 s - v) (c + 2 f Sqrt[z]) Gamma[(1/2) (1 + h + k), -(((2 s - v) (c + 2 f Sqrt[z])^2)/ (4 f))] + 2 f Sqrt[-(((2 s - v) (c + 2 f Sqrt[z])^2)/f)] Gamma[(1/2) (2 + h + k), -(((2 s - v) (c + 2 f Sqrt[z])^2)/ (4 f))]), {k, 0, n}, {h, 0, k}]))/ E^(((-c^2 + 4 f g) (2 s - v))/(4 f)), {s, 0, Floor[(1/2) (-1 + v)]}])/(2^(2 n) I^m f^(2 (1 + n)))) + ((-1)^m Sum[(-1)^u Binomial[m, u] Sum[(E^(e m + 2 g s - 2 e u - g v) Binomial[v, s] ((Sum[(-1)^(-h + k) 4^k ((-b) m + 2 c s + 2 b u - c v)^(-h - k + 2 n) (-((b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/(f (2 s - v))))^((1/2) (-1 - h - k)) ((-b) (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^(h + k) Binomial[k, h] Binomial[n, k] ((b (m - 2 u) + c (-2 s + v)) (b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z])) Gamma[(1/2) (1 + h + k), -((b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (8 s - 4 v)))] - 2 f (-2 s + v) Sqrt[ -((b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (2 s - v)))] Gamma[(1/2) (2 + h + k), -((b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (8 s - 4 v)))]), {k, 0, n}, {h, 0, k}]/E^ (2 e (m - 2 u)) + (-1)^m E^(-4 g s + 2 g v + (b (m - 2 u) + c (-2 s + v))^2/(f (4 s - 2 v))) Sum[ (-1)^(-h + k) 4^k (b (m - 2 u) + c (-2 s + v))^(-h - k + 2 n) (b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^(h + k) ((b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (2 s - v)))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((b (m - 2 u) + c (-2 s + v)) (b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z])) Gamma[(1/2) (1 + h + k), (b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (8 s - 4 v))] + 2 f (-2 s + v) Sqrt[(b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/(f (2 s - v))] Gamma[(1/2) (2 + h + k), (b (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^2/(f (8 s - 4 v))]), {k, 0, n}, {h, 0, k}])/E^((b (m - 2 u) + c (-2 s + v))^2/(f (8 s - 4 v))) + ((-1)^m Sum[(-1)^(-h + k) 4^k (b m + 2 c s - 2 b u - c v)^(-h - k + 2 n) (b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^(h + k) (-((b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (2 s - v))))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((b m + 2 c s - 2 b u - c v) (b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z])) Gamma[(1/2) (1 + h + k), -((b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (8 s - 4 v)))] + 2 f (2 s - v) Sqrt[ -((b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (2 s - v)))] Gamma[(1/2) (2 + h + k), -((b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (8 s - 4 v)))]), {k, 0, n}, {h, 0, k}])/ E^((b m + 2 c s - 2 b u - c v)^2/(f (8 s - 4 v))) + E^(-2 e (m - 2 u) + 2 g (-2 s + v) + (b m + 2 c s - 2 b u - c v)^ 2/(f (8 s - 4 v))) Sum[(-1)^(-h + k) 4^k ((-b) m - 2 c s + 2 b u + c v)^(-h - k + 2 n) ((-b) (m - 2 u) - (2 s - v) (c + 2 f Sqrt[z]))^(h + k) ((b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/(f (2 s - v)))^((1/2) (-1 - h - k)) Binomial[k, h] Binomial[n, k] ((b m + 2 c s - 2 b u - c v) (b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z])) Gamma[ (1/2) (1 + h + k), (b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/(f (8 s - 4 v))] - 2 f (2 s - v) Sqrt[(b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (2 s - v))] Gamma[(1/2) (2 + h + k), (b (m - 2 u) + (2 s - v) (c + 2 f Sqrt[z]))^2/ (f (8 s - 4 v))]), {k, 0, n}, {h, 0, k}]))/ (-2 s + v)^(2 (1 + n)), {s, 0, Floor[(1/2) (-1 + v)]}], {u, 0, Floor[(1/2) (-1 + m)]}])/(2^(2 n) f^(2 (1 + n)))) /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 z n sinh m ( z b + e ) cosh v ( z c + g + f z ) z 2 - m - v - 1 ( 2 - m z 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]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) ( v mod 2 \$CellContext`v 2 - 1 ) n + 1 - 4 b - 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 ) k = 0 m - 1 2 ( - 1 ) k - 2 e k - e m ( m - 2 k ) - 2 ( n + 1 ) ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - 1 ) m 4 e k Γ ( 2 ( n + 1 ) , - b ( 2 k - m ) z ) + 2 e m Γ ( 2 ( n + 1 ) , b ( 2 k - m ) z ) ) - 1 c ( 2 - 2 n - m f - 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 ) s = 0 v - 1 2 - ( 4 f g - c 2 ) ( 2 s - v ) 4 f ( v - 2 s ) - 2 n - 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( k = 0 n h = 0 k ( - 1 ) k - h 4 k c ( 2 s - v ) ( c ( v - 2 s ) ) - h - k + 2 n ( - ( 2 s - v ) ( c + 2 f z ) ) h + k ( ( 2 s - v ) ( c + 2 f z ) 2 f ) 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]]]]] ( c ( 2 s - v ) ( c + 2 f z ) Γ ( 1 2 ( h + k + 1 ) , ( 2 s - v ) ( c + 2 f z ) 2 4 f ) - 2 f ( 2 s - v ) ( c + 2 f z ) 2 f Γ ( 1 2 ( h + k + 2 ) , ( 2 s - v ) ( c + 2 f z ) 2 4 f ) ) + ( 4 f g - c 2 ) ( 2 s - v ) 2 f k = 0 n h = 0 k ( - 1 ) k - h 4 k ( c ( 2 s - v ) ) - h - k + 2 n + 1 ( ( 2 s - v ) ( c + 2 f z ) ) h + k ( - ( 2 s - v ) ( c + 2 f z ) 2 f ) 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]]]]] ( c ( 2 s - v ) ( c + 2 f z ) Γ ( 1 2 ( h + k + 1 ) , - ( 2 s - v ) ( c + 2 f z ) 2 4 f ) + 2 - ( 2 s - v ) ( c + 2 f z ) 2 f f Γ ( 1 2 ( h + k + 2 ) , - ( 2 s - v ) ( c + 2 f z ) 2 4 f ) ) ) ) + 2 - 2 n ( - 1 ) m f - 2 ( n + 1 ) 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]]]]] s = 0 v - 1 2 e m + 2 g s - 2 e u - g v ( 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]]]]] ( ( b m + 2 c s - 2 b u - c v ) 2 f ( 8 s - 4 v ) - 2 e ( m - 2 u ) + 2 g ( v - 2 s ) k = 0 n h = 0 k ( - 1 ) k - h 4 k ( - b m - 2 c s + 2 b u + c v ) - h - k + 2 n ( - b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) h + k ( ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 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 + 2 c s - 2 b u - c v ) ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) Γ ( 1 2 ( h + k + 1 ) , ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) - 2 f ( 2 s - v ) ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 2 s - v ) Γ ( 1 2 ( h + k + 2 ) , ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) ) + - ( b ( m - 2 u ) + c ( v - 2 s ) ) 2 f ( 8 s - 4 v ) ( ( - 1 ) m ( b ( m - 2 u ) + c ( v - 2 s ) ) 2 f ( 4 s - 2 v ) - 4 g s + 2 g v k = 0 n h = 0 k ( - 1 ) k - h 4 k ( b ( m - 2 u ) + c ( v - 2 s ) ) - h - k + 2 n ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) h + k ( ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 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 - 2 u ) + c ( v - 2 s ) ) ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) Γ ( 1 2 ( h + k + 1 ) , ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) + 2 f ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 2 s - v ) ( v - 2 s ) Γ ( 1 2 ( h + k + 2 ) , ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) ) + - 2 e ( m - 2 u ) k = 0 n h = 0 k ( - 1 ) k - h 4 k ( - b m + 2 c s + 2 b u - c v ) - h - k + 2 n ( - ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 2 s - v ) ) 1 2 ( - h - k - 1 ) ( ( 2 s - v ) ( c + 2 f 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]]]]] ( ( b ( m - 2 u ) + c ( v - 2 s ) ) ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) Γ ( 1 2 ( h + k + 1 ) , - ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) - 2 f ( v - 2 s ) - ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 2 s - v ) Γ ( 1 2 ( h + k + 2 ) , - ( b ( m - 2 u ) - ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) ) ) + ( - 1 ) m - ( b m + 2 c s - 2 b u - c v ) 2 f ( 8 s - 4 v ) k = 0 n h = 0 k ( - 1 ) k - h 4 k ( b m + 2 c s - 2 b u - c v ) - h - k + 2 n ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) h + k ( - ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 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 + 2 c s - 2 b u - c v ) ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) Γ ( 1 2 ( h + k + 1 ) , - ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) + 2 f ( 2 s - v ) - ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 2 s - v ) Γ ( 1 2 ( h + k + 2 ) , - ( b ( m - 2 u ) + ( 2 s - v ) ( c + 2 f z ) ) 2 f ( 8 s - 4 v ) ) ) ) ) /; n m + v + Condition z z n z 1 2 b e m z 1 2 c g f z v 2 -1 m -1 v -1 2 -1 m z n 1 Binomial m m 2 -1 Binomial v v 2 -1 \$CellContext`m 2 -1 \$CellContext`v 2 -1 n 1 -1 -1 4 b -2 n 1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k -2 e k -1 e m m -1 2 k -2 n 1 Binomial m k -1 m 4 e k Gamma 2 n 1 -1 b 2 k -1 m z 1 2 2 e m Gamma 2 n 1 b 2 k -1 m z 1 2 -1 1 c -1 2 -2 n -1 m f -2 n 1 Binomial m m 2 -1 \$CellContext`m 2 -1 s 0 v -1 2 -1 -1 4 f g -1 c 2 2 s -1 v 4 f -1 v -1 2 s -2 n -2 Binomial v s h 0 k k 0 n -1 k -1 h 4 k c 2 s -1 v c v -1 2 s -1 h -1 k 2 n -1 2 s -1 v c 2 f z 1 2 h k 2 s -1 v c 2 f z 1 2 2 f -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k c 2 s -1 v c 2 f z 1 2 Gamma 1 2 h k 1 2 s -1 v c 2 f z 1 2 2 4 f -1 -1 2 f 2 s -1 v c 2 f z 1 2 2 f -1 1 2 Gamma 1 2 h k 2 2 s -1 v c 2 f z 1 2 2 4 f -1 4 f g -1 c 2 2 s -1 v 2 f -1 h 0 k k 0 n -1 k -1 h 4 k c 2 s -1 v -1 h -1 k 2 n 1 2 s -1 v c 2 f z 1 2 h k -1 2 s -1 v c 2 f z 1 2 2 f -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k c 2 s -1 v c 2 f z 1 2 Gamma 1 2 h k 1 -1 2 s -1 v c 2 f z 1 2 2 4 f -1 2 -1 2 s -1 v c 2 f z 1 2 2 f -1 1 2 f Gamma 1 2 h k 2 -1 2 s -1 v c 2 f z 1 2 2 4 f -1 2 -2 n -1 m f -2 n 1 u 0 m -1 2 -1 -1 u Binomial m u s 0 v -1 2 -1 e m 2 g s -1 2 e u -1 g v v -1 2 s -2 n 1 Binomial v s b m 2 c s -1 2 b u -1 c v 2 f 8 s -1 4 v -1 -1 2 e m -1 2 u 2 g v -1 2 s h 0 k k 0 n -1 k -1 h 4 k -1 b m -1 2 c s 2 b u c v -1 h -1 k 2 n -1 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 h k b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b m 2 c s -1 2 b u -1 c v b m -1 2 u 2 s -1 v c 2 f z 1 2 Gamma 1 2 h k 1 b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 -1 2 f 2 s -1 v b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 Gamma 1 2 h k 2 b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 -1 b m -1 2 u c v -1 2 s 2 f 8 s -1 4 v -1 -1 m b m -1 2 u c v -1 2 s 2 f 4 s -1 2 v -1 -1 4 g s 2 g v h 0 k k 0 n -1 k -1 h 4 k b m -1 2 u c v -1 2 s -1 h -1 k 2 n b m -1 2 u -1 2 s -1 v c 2 f z 1 2 h k b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b m -1 2 u c v -1 2 s b m -1 2 u -1 2 s -1 v c 2 f z 1 2 Gamma 1 2 h k 1 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 2 f b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 v -1 2 s Gamma 1 2 h k 2 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 -2 e m -1 2 u h 0 k k 0 n -1 k -1 h 4 k -1 b m 2 c s 2 b u -1 c v -1 h -1 k 2 n -1 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 -1 h -1 k -1 2 s -1 v c 2 f z 1 2 -1 b m -1 2 u h k Binomial k h Binomial n k b m -1 2 u c v -1 2 s b m -1 2 u -1 2 s -1 v c 2 f z 1 2 Gamma 1 2 h k 1 -1 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 -1 2 f v -1 2 s -1 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 Gamma 1 2 h k 2 -1 b m -1 2 u -1 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 -1 m -1 b m 2 c s -1 2 b u -1 c v 2 f 8 s -1 4 v -1 h 0 k k 0 n -1 k -1 h 4 k b m 2 c s -1 2 b u -1 c v -1 h -1 k 2 n b m -1 2 u 2 s -1 v c 2 f z 1 2 h k -1 b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b m 2 c s -1 2 b u -1 c v b m -1 2 u 2 s -1 v c 2 f z 1 2 Gamma 1 2 h k 1 -1 b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 2 f 2 s -1 v -1 b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 2 s -1 v -1 1 2 Gamma 1 2 h k 2 -1 b m -1 2 u 2 s -1 v c 2 f z 1 2 2 f 8 s -1 4 v -1 n m SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18