html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.1164.01

 Input Form

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

 Standard Form

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"+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "j"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["f", "+", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "j"]], "+", "m"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["f", "+", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "j"]], "+", "m"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]]]], "]"]], "m_"], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m", "-", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox["f", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "f"]]]], " ", 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["-", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "k", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "k"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], "2"], "f"], ")"]], 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["-", "c"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "f", " ", 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["-", "c"]], "-", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", "f"]]]]], "]"]]]], "-", RowBox[List["2", " ", "f", " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], "2"], "f"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "k"]], ")"]]]], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", "f"]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "f"]]]]]], " ", 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["c", RowBox[List[RowBox[List["-", "h"]], "-", "k", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "k"]]], " ", SuperscriptBox[RowBox[List["(", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18