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 Cosh

 http://functions.wolfram.com/01.20.21.4518.01

 Input Form

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

 Standard Form

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 MathML Form

 z n sinh ( z b + d z + e ) cosh v ( z c + f z + g ) z 2 - 2 n - v - 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]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) d - 2 n - 2 ( e - b 2 4 d k = 0 n h = 0 k ( - 1 ) k - h 4 k b - h - k + 2 n ( b + 2 d z ) h + k ( - ( b + 2 d z ) 2 d ) 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 ( b + 2 d z ) Γ ( 1 2 ( h + k + 1 ) , - ( b + 2 d z ) 2 4 d ) + 2 - ( b + 2 d z ) 2 d d Γ ( 1 2 ( h + k + 2 ) , - ( b + 2 d z ) 2 4 d ) ) - b 2 4 d - e k = 0 n h = 0 k ( - 1 ) k - h 4 k ( - b ) - h - k + 2 n ( - b - 2 d z ) h + k ( ( - b - 2 d z ) 2 d ) 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 ( - b - 2 d z ) Γ ( 1 2 ( h + k + 1 ) , ( - b - 2 d z ) 2 4 d ) - 2 d ( - b - 2 d z ) 2 d Γ ( 1 2 ( h + k + 2 ) , ( - b - 2 d z ) 2 4 d ) ) ) + 2 - 2 n - v - 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]]]]] ( - - ( c ( 2 s - v ) - b ) 2 4 ( f ( 2 s - v ) - d ) - e + g ( 2 s - v ) ( f ( 2 s - v ) - d ) - 2 n - 2 k = 0 n h = 0 k ( - 1 ) k - h 4 k ( c ( 2 s - v ) - b ) - h - k + 2 n ( - b + c ( 2 s - v ) + 2 ( f ( 2 s - v ) - d ) z ) h + k ( - ( - b + c ( 2 s - v ) + 2 ( f ( 2 s - v ) - d ) z ) 2 f ( 2 s - v ) - d ) 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 ) - b ) ( - b + c ( 2 s - v ) + 2 ( f ( 2 s - v ) - d ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( - b + c ( 2 s - v ) + 2 ( f ( 2 s - v ) - d ) z ) 2 4 ( f ( 2 s - v ) - d ) ) + 2 - ( - b + c ( 2 s - v ) + 2 ( f ( 2 s - v ) - d ) z ) 2 f ( 2 s - v ) - d ( f ( 2 s - v ) - d ) Γ ( 1 2 ( h + k + 2 ) , - ( - b + c ( 2 s - v ) + 2 ( f ( 2 s - v ) - d ) z ) 2 4 ( f ( 2 s - v ) - d ) ) ) + - ( b + c ( 2 s - v ) ) 2 4 ( d + f ( 2 s - v ) ) + e + g ( 2 s - v ) ( d + f ( 2 s - v ) ) - 2 n - 2 k = 0 n h = 0 k ( - 1 ) k - h 4 k ( b + c ( 2 s - v ) ) - h - k + 2 n ( b + c ( 2 s - v ) + 2 ( d + f ( 2 s - v ) ) z ) h + k ( - ( b + c ( 2 s - v ) + 2 ( d + f ( 2 s - v ) ) z ) 2 d + 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 + c ( 2 s - v ) ) ( b + c ( 2 s - v ) + 2 ( d + f ( 2 s - v ) ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( b + c ( 2 s - v ) + 2 ( d + f ( 2 s - v ) ) z ) 2 4 ( d + f ( 2 s - v ) ) ) + 2 - ( b + c ( 2 s - v ) + 2 ( d + f ( 2 s - v ) ) z ) 2 d + f ( 2 s - v ) ( d + f ( 2 s - v ) ) Γ ( 1 2 ( h + k + 2 ) , - ( b + c ( 2 s - v ) + 2 ( d + f ( 2 s - v ) ) z ) 2 4 ( d + f ( 2 s - v ) ) ) ) - - ( c ( v - 2 s ) - b ) 2 4 ( f ( v - 2 s ) - d ) - e + g ( v - 2 s ) ( f ( v - 2 s ) - d ) - 2 n - 2 k = 0 n h = 0 k ( - 1 ) k - h 4 k ( c ( v - 2 s ) - b ) - h - k + 2 n ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z ) h + k ( - ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z ) 2 f ( v - 2 s ) - d ) 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 ( v - 2 s ) - b ) ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z ) 2 4 ( f ( v - 2 s ) - d ) ) + 2 - ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z ) 2 f ( v - 2 s ) - d ( f ( v - 2 s ) - d ) Γ ( 1 2 ( h + k + 2 ) , - ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z ) 2 4 ( f ( v - 2 s ) - d ) ) ) + - ( b + c ( v - 2 s ) ) 2 4 ( d + f ( v - 2 s ) ) + e + g ( v - 2 s ) ( d + f ( v - 2 s ) ) - 2 n - 2 k = 0 n h = 0 k ( - 1 ) k - h 4 k ( b + c ( v - 2 s ) ) - h - k + 2 n ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z ) h + k ( - ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z ) 2 d + f ( 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]]]]] ( ( b + c ( v - 2 s ) ) ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z ) Γ ( 1 2 ( h + k + 1 ) , - ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z ) 2 4 ( d + f ( v - 2 s ) ) ) + 2 - ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z ) 2 d + f ( v - 2 s ) ( d + f ( v - 2 s ) ) Γ ( 1 2 ( h + k + 2 ) , - ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z ) 2 4 ( d + f ( v - 2 s ) ) ) ) ) /; n v + Condition z z n z 1 2 b d z e z 1 2 c f z g v 2 -2 n -1 v -2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 d -2 n -2 e -1 b 2 4 d -1 h 0 k k 0 n -1 k -1 h 4 k b -1 h -1 k 2 n b 2 d z 1 2 h k -1 b 2 d z 1 2 2 d -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b b 2 d z 1 2 Gamma 1 2 h k 1 -1 b 2 d z 1 2 2 4 d -1 2 -1 b 2 d z 1 2 2 d -1 1 2 d Gamma 1 2 h k 2 -1 b 2 d z 1 2 2 4 d -1 -1 b 2 4 d -1 -1 e h 0 k k 0 n -1 k -1 h 4 k -1 b -1 h -1 k 2 n -1 b -1 2 d z 1 2 h k -1 b -1 2 d z 1 2 2 d -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k -1 b -1 b -1 2 d z 1 2 Gamma 1 2 h k 1 -1 b -1 2 d z 1 2 2 4 d -1 -1 2 d -1 b -1 2 d z 1 2 2 d -1 1 2 Gamma 1 2 h k 2 -1 b -1 2 d z 1 2 2 4 d -1 2 -2 n -1 v -2 s 0 v -1 2 -1 Binomial v s -1 -1 c 2 s -1 v -1 b 2 4 f 2 s -1 v -1 d -1 -1 e g 2 s -1 v f 2 s -1 v -1 d -2 n -2 h 0 k k 0 n -1 k -1 h 4 k c 2 s -1 v -1 b -1 h -1 k 2 n -1 b c 2 s -1 v 2 f 2 s -1 v -1 d z 1 2 h k -1 -1 b c 2 s -1 v 2 f 2 s -1 v -1 d z 1 2 2 f 2 s -1 v -1 d -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k c 2 s -1 v -1 b -1 b c 2 s -1 v 2 f 2 s -1 v -1 d z 1 2 Gamma 1 2 h k 1 -1 -1 b c 2 s -1 v 2 f 2 s -1 v -1 d z 1 2 2 4 f 2 s -1 v -1 d -1 2 -1 -1 b c 2 s -1 v 2 f 2 s -1 v -1 d z 1 2 2 f 2 s -1 v -1 d -1 1 2 f 2 s -1 v -1 d Gamma 1 2 h k 2 -1 -1 b c 2 s -1 v 2 f 2 s -1 v -1 d z 1 2 2 4 f 2 s -1 v -1 d -1 -1 b c 2 s -1 v 2 4 d f 2 s -1 v -1 e g 2 s -1 v d f 2 s -1 v -2 n -2 h 0 k k 0 n -1 k -1 h 4 k b c 2 s -1 v -1 h -1 k 2 n b c 2 s -1 v 2 d f 2 s -1 v z 1 2 h k -1 b c 2 s -1 v 2 d f 2 s -1 v z 1 2 2 d f 2 s -1 v -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b c 2 s -1 v b c 2 s -1 v 2 d f 2 s -1 v z 1 2 Gamma 1 2 h k 1 -1 b c 2 s -1 v 2 d f 2 s -1 v z 1 2 2 4 d f 2 s -1 v -1 2 -1 b c 2 s -1 v 2 d f 2 s -1 v z 1 2 2 d f 2 s -1 v -1 1 2 d f 2 s -1 v Gamma 1 2 h k 2 -1 b c 2 s -1 v 2 d f 2 s -1 v z 1 2 2 4 d f 2 s -1 v -1 -1 -1 c v -1 2 s -1 b 2 4 f v -1 2 s -1 d -1 -1 e g v -1 2 s f v -1 2 s -1 d -2 n -2 h 0 k k 0 n -1 k -1 h 4 k c v -1 2 s -1 b -1 h -1 k 2 n -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 h k -1 -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 f v -1 2 s -1 d -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k c v -1 2 s -1 b -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 Gamma 1 2 h k 1 -1 -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 4 f v -1 2 s -1 d -1 2 -1 -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 f v -1 2 s -1 d -1 1 2 f v -1 2 s -1 d Gamma 1 2 h k 2 -1 -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 4 f v -1 2 s -1 d -1 -1 b c v -1 2 s 2 4 d f v -1 2 s -1 e g v -1 2 s d f v -1 2 s -2 n -2 h 0 k k 0 n -1 k -1 h 4 k b c v -1 2 s -1 h -1 k 2 n b c v -1 2 s 2 d f v -1 2 s z 1 2 h k -1 b c v -1 2 s 2 d f v -1 2 s z 1 2 2 d f v -1 2 s -1 1 2 -1 h -1 k -1 Binomial k h Binomial n k b c v -1 2 s b c v -1 2 s 2 d f v -1 2 s z 1 2 Gamma 1 2 h k 1 -1 b c v -1 2 s 2 d f v -1 2 s z 1 2 2 4 d f v -1 2 s -1 2 -1 b c v -1 2 s 2 d f v -1 2 s z 1 2 2 d f v -1 2 s -1 1 2 d f v -1 2 s Gamma 1 2 h k 2 -1 b c v -1 2 s 2 d f v -1 2 s z 1 2 2 4 d f v -1 2 s -1 n v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", SuperscriptBox["d", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", "d"]]], "-", "e"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "k"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "k"]]], " ", SuperscriptBox["4", "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "k", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "k"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"], "d"], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "k"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["k", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "k"]], ")"]]]], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", "d"]]]]], "]"]]]], "-", RowBox[List["2", " ", "d", " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], ")"]], "2"], "d"]], " 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18