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 Cosh

 http://functions.wolfram.com/01.20.21.1027.01

 Input Form

 Integrate[z^n Sin[b Sqrt[z] + d z]^m Cosh[c Sqrt[z] + f z + g], z] == 2^(-2 - m - 2 n) f^(-2 - 2 n) Binomial[m, m/2] (1 - Mod[m, 2]) (E^(c^2/(4 f) - g) Sum[(-1)^(-h + j) 4^j (-c)^(-h - j + 2 n) (-c - 2 f Sqrt[z])^(h + j) ((-c - 2 f Sqrt[z])^2/f)^ ((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c) (-c - 2 f Sqrt[z]) Gamma[(1/2) (1 + h + j), (-c - 2 f Sqrt[z])^2/(4 f)] - 2 f Sqrt[(-c - 2 f Sqrt[z])^2/f] Gamma[(1/2) (2 + h + j), (-c - 2 f Sqrt[z])^2/(4 f)]), {j, 0, n}, {h, 0, j}] + E^(-(c^2/(4 f)) + g) Sum[(-1)^(-h + j) 4^j c^(-h - j + 2 n) (c + 2 f Sqrt[z])^(h + j) (-((c + 2 f Sqrt[z])^2/f))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] (c (c + 2 f Sqrt[z]) Gamma[(1/2) (1 + h + j), -((c + 2 f Sqrt[z])^2/(4 f))] + 2 f Sqrt[-((c + 2 f Sqrt[z])^2/f)] Gamma[(1/2) (2 + h + j), -((c + 2 f Sqrt[z])^2/(4 f))]), {j, 0, n}, {h, 0, j}]) + 2^(-2 - m - 2 n) Sum[(-1)^s Binomial[m, s] (E^(-g - (I m Pi)/2 - (-c + I b (m - 2 s))^2/(4 (-f + I d (m - 2 s)))) (-f + I d (m - 2 s))^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j (-c + I b (m - 2 s))^(-h - j + 2 n) (-c + I b (m - 2 s) + 2 (-f + I d (m - 2 s)) Sqrt[z])^(h + j) (-((-c + I b (m - 2 s) + 2 (-f + I d (m - 2 s)) Sqrt[z])^2/ (-f + I d (m - 2 s))))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c + I b (m - 2 s)) (-c + I b (m - 2 s) + 2 (-f + I d (m - 2 s)) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((-c + I b (m - 2 s) + 2 (-f + I d (m - 2 s)) Sqrt[z])^2/(4 (-f + I d (m - 2 s))))] + 2 (-f + I d (m - 2 s)) Sqrt[-((-c + I b (m - 2 s) + 2 (-f + I d (m - 2 s)) Sqrt[z])^2/( -f + I d (m - 2 s)))] Gamma[(1/2) (2 + h + j), -((-c + I b (m - 2 s) + 2 (-f + I d (m - 2 s)) Sqrt[z])^2/(4 (-f + I d (m - 2 s))))]), {j, 0, n}, {h, 0, j}] + E^(g - (I m Pi)/2 - (c + I b (m - 2 s))^2/(4 (f + I d (m - 2 s)))) (f + I d (m - 2 s))^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j (c + I b (m - 2 s))^(-h - j + 2 n) (c + I b (m - 2 s) + 2 (f + I d (m - 2 s)) Sqrt[z])^(h + j) (-((c + I b (m - 2 s) + 2 (f + I d (m - 2 s)) Sqrt[z])^2/ (f + I d (m - 2 s))))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((c + I b (m - 2 s)) (c + I b (m - 2 s) + 2 (f + I d (m - 2 s)) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((c + I b (m - 2 s) + 2 (f + I d (m - 2 s)) Sqrt[z])^2/(4 (f + I d (m - 2 s))))] + 2 (f + I d (m - 2 s)) Sqrt[-((c + I b (m - 2 s) + 2 (f + I d (m - 2 s)) Sqrt[z])^2/(f + I d (m - 2 s)))] Gamma[(1/2) (2 + h + j), -((c + I b (m - 2 s) + 2 (f + I d (m - 2 s)) Sqrt[z])^2/(4 (f + I d (m - 2 s))))]), {j, 0, n}, {h, 0, j}] + E^(-g + (I m Pi)/2 - (-c + I b (-m + 2 s))^2/ (4 (-f + I d (-m + 2 s)))) (-f + I d (-m + 2 s))^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j (-c + I b (-m + 2 s))^(-h - j + 2 n) (-c + I b (-m + 2 s) + 2 (-f + I d (-m + 2 s)) Sqrt[z])^(h + j) (-((-c + I b (-m + 2 s) + 2 (-f + I d (-m + 2 s)) Sqrt[z])^2/ (-f + I d (-m + 2 s))))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c + I b (-m + 2 s)) (-c + I b (-m + 2 s) + 2 (-f + I d (-m + 2 s)) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((-c + I b (-m + 2 s) + 2 (-f + I d (-m + 2 s)) Sqrt[z])^2/(4 (-f + I d (-m + 2 s))))] + 2 (-f + I d (-m + 2 s)) Sqrt[-((-c + I b (-m + 2 s) + 2 (-f + I d (-m + 2 s)) Sqrt[z])^2/( -f + I d (-m + 2 s)))] Gamma[(1/2) (2 + h + j), -((-c + I b (-m + 2 s) + 2 (-f + I d (-m + 2 s)) Sqrt[z])^2/(4 (-f + I d (-m + 2 s))))]), {j, 0, n}, {h, 0, j}] + E^(g + (I m Pi)/2 - (c + I b (-m + 2 s))^2/(4 (f + I d (-m + 2 s)))) (f + I d (-m + 2 s))^(-2 - 2 n) Sum[(-1)^(-h + j) 4^j (c + I b (-m + 2 s))^(-h - j + 2 n) (c + I b (-m + 2 s) + 2 (f + I d (-m + 2 s)) Sqrt[z])^(h + j) (-((c + I b (-m + 2 s) + 2 (f + I d (-m + 2 s)) Sqrt[z])^2/ (f + I d (-m + 2 s))))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((c + I b (-m + 2 s)) (c + I b (-m + 2 s) + 2 (f + I d (-m + 2 s)) Sqrt[z]) Gamma[(1/2) (1 + h + j), -((c + I b (-m + 2 s) + 2 (f + I d (-m + 2 s)) Sqrt[z])^2/(4 (f + I d (-m + 2 s))))] + 2 (f + I d (-m + 2 s)) Sqrt[-((c + I b (-m + 2 s) + 2 (f + I d (-m + 2 s)) Sqrt[z])^2/( f + I d (-m + 2 s)))] Gamma[(1/2) (2 + h + j), -((c + I b (-m + 2 s) + 2 (f + I d (-m + 2 s)) Sqrt[z])^2/(4 (f + I d (-m + 2 s))))]), {j, 0, n}, {h, 0, j}]), {s, 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]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["f", "+", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "j"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["f", "+", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["f", "+", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "m"]], "+", RowBox[List["2", " ", "s"]]]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]]]], "/;", 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 sin m ( z b + d z ) cosh ( z c + g + 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 - g j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - c ) - h - j + 2 n ( - c - 2 f z ) h + j ( ( - c - 2 f z ) 2 f ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - c ( - c - 2 f z ) Γ ( 1 2 ( h + j + 1 ) , ( - c - 2 f z ) 2 4 f ) - 2 f ( - c - 2 f z ) 2 f Γ ( 1 2 ( h + j + 2 ) , ( - c - 2 f z ) 2 4 f ) ) + g - c 2 4 f j = 0 n h = 0 j ( - 1 ) j - h 4 j c - h - j + 2 n ( c + 2 f z ) h + j ( - ( c + 2 f z ) 2 f ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( c + 2 f z ) Γ ( 1 2 ( h + j + 1 ) , - ( c + 2 f z ) 2 4 f ) + 2 - ( c + 2 f z ) 2 f f Γ ( 1 2 ( h + j + 2 ) , - ( c + 2 f z ) 2 4 f ) ) ) f - 2 n - 2 + 2 - m - 2 n - 2 s = 0 m - 1 2 ( - 1 ) s ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( b ( 2 s - m ) - c ) 2 4 ( d ( 2 s - m ) - f ) - g + m π 2 ( j = 0 n h = 0 j ( - 1 ) j - h 4 j ( b ( 2 s - m ) - c ) - h - j + 2 n ( - c + b ( 2 s - m ) + 2 ( d ( 2 s - m ) - f ) z ) h + j ( - ( - c + b ( 2 s - m ) + 2 ( d ( 2 s - m ) - f ) z ) 2 d ( 2 s - m ) - f ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b ( 2 s - m ) - c ) ( - c + b ( 2 s - m ) + 2 ( d ( 2 s - m ) - f ) z ) Γ ( 1 2 ( h + j + 1 ) , - ( - c + b ( 2 s - m ) + 2 ( d ( 2 s - m ) - f ) z ) 2 4 ( d ( 2 s - m ) - f ) ) + 2 ( d ( 2 s - m ) - f ) Γ ( 1 2 ( h + j + 2 ) , - ( - c + b ( 2 s - m ) + 2 ( d ( 2 s - m ) - f ) z ) 2 4 ( d ( 2 s - m ) - f ) ) - ( - c + b ( 2 s - m ) + 2 ( d ( 2 s - m ) - f ) z ) 2 d ( 2 s - m ) - f ) ) ( d ( 2 s - m ) - f ) - 2 n - 2 + - ( c + b ( 2 s - m ) ) 2 4 ( f + d ( 2 s - m ) ) + g + m π 2 ( f + d ( 2 s - m ) ) - 2 n - 2 j = 0 n h = 0 j ( - 1 ) j - h 4 j ( c + b ( 2 s - m ) ) - h - j + 2 n ( c + b ( 2 s - m ) + 2 ( f + d ( 2 s - m ) ) z ) h + j ( - ( c + b ( 2 s - m ) + 2 ( f + d ( 2 s - m ) ) z ) 2 f + d ( 2 s - m ) ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( c + b ( 2 s - m ) ) ( c + b ( 2 s - m ) + 2 ( f + d ( 2 s - m ) ) z ) Γ ( 1 2 ( h + j + 1 ) , - ( c + b ( 2 s - m ) + 2 ( f + d ( 2 s - m ) ) z ) 2 4 ( f + d ( 2 s - m ) ) ) + 2 - ( c + b ( 2 s - m ) + 2 ( f + d ( 2 s - m ) ) z ) 2 f + d ( 2 s - m ) ( f + d ( 2 s - m ) ) Γ ( 1 2 ( h + j + 2 ) , - ( c + b ( 2 s - m ) + 2 ( f + d ( 2 s - m ) ) z ) 2 4 ( f + d ( 2 s - m ) ) ) ) + - ( b ( m - 2 s ) - c ) 2 4 ( d ( m - 2 s ) - f ) - g - m π 2 ( d ( m - 2 s ) - f ) - 2 n - 2 j = 0 n h = 0 j ( - 1 ) j - h 4 j ( b ( m - 2 s ) - c ) - h - j + 2 n ( - c + b ( m - 2 s ) + 2 ( d ( m - 2 s ) - f ) z ) h + j ( - ( - c + b ( m - 2 s ) + 2 ( d ( m - 2 s ) - f ) z ) 2 d ( m - 2 s ) - f ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b ( m - 2 s ) - c ) ( - c + b ( m - 2 s ) + 2 ( d ( m - 2 s ) - f ) z ) Γ ( 1 2 ( h + j + 1 ) , - ( - c + b ( m - 2 s ) + 2 ( d ( m - 2 s ) - f ) z ) 2 4 ( d ( m - 2 s ) - f ) ) + 2 - ( - c + b ( m - 2 s ) + 2 ( d ( m - 2 s ) - f ) z ) 2 d ( m - 2 s ) - f ( d ( m - 2 s ) - f ) Γ ( 1 2 ( h + j + 2 ) , - ( - c + b ( m - 2 s ) + 2 ( d ( m - 2 s ) - f ) z ) 2 4 ( d ( m - 2 s ) - f ) ) ) + - ( c + b ( m - 2 s ) ) 2 4 ( f + d ( m - 2 s ) ) + g - m π 2 ( f + d ( m - 2 s ) ) - 2 n - 2 j = 0 n h = 0 j ( - 1 ) j - h 4 j ( c + b ( m - 2 s ) ) - h - j + 2 n ( c + b ( m - 2 s ) + 2 ( f + d ( m - 2 s ) ) z ) h + j ( - ( c + b ( m - 2 s ) + 2 ( f + d ( m - 2 s ) ) z ) 2 f + d ( m - 2 s ) ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( c + b ( m - 2 s ) ) ( c + b ( m - 2 s ) + 2 ( f + d ( m - 2 s ) ) z ) Γ ( 1 2 ( h + j + 1 ) , - ( c + b ( m - 2 s ) + 2 ( f + d ( m - 2 s ) ) z ) 2 4 ( f + d ( m - 2 s ) ) ) + 2 - ( c + b ( m - 2 s ) + 2 ( f + d ( m - 2 s ) ) z ) 2 f + d ( m - 2 s ) ( f + d ( m - 2 s ) ) Γ ( 1 2 ( h + j + 2 ) , - ( c + b ( m - 2 s ) + 2 ( f + d ( m - 2 s ) ) z ) 2 4 ( f + d ( m - 2 s ) ) ) ) ) /; n m + Condition z z n z 1 2 b d z m z 1 2 c g f z 2 -1 m -1 2 n -2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 c 2 4 f -1 -1 g h 0 j j 0 n -1 j -1 h 4 j -1 c -1 h -1 j 2 n -1 c -1 2 f z 1 2 h j -1 c -1 2 f z 1 2 2 f -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j -1 c -1 c -1 2 f z 1 2 Gamma 1 2 h j 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 j 2 -1 c -1 2 f z 1 2 2 4 f -1 g -1 c 2 4 f -1 h 0 j j 0 n -1 j -1 h 4 j c -1 h -1 j 2 n c 2 f z 1 2 h j -1 c 2 f z 1 2 2 f -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c c 2 f z 1 2 Gamma 1 2 h j 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 j 2 -1 c 2 f z 1 2 2 4 f -1 f -2 n -2 2 -1 m -1 2 n -2 s 0 m -1 2 -1 -1 s Binomial m s -1 b 2 s -1 m -1 c 2 4 d 2 s -1 m -1 f -1 -1 g m 2 -1 h 0 j j 0 n -1 j -1 h 4 j b 2 s -1 m -1 c -1 h -1 j 2 n -1 c b 2 s -1 m 2 d 2 s -1 m -1 f z 1 2 h j -1 -1 c b 2 s -1 m 2 d 2 s -1 m -1 f z 1 2 2 d 2 s -1 m -1 f -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j b 2 s -1 m -1 c -1 c b 2 s -1 m 2 d 2 s -1 m -1 f z 1 2 Gamma 1 2 h j 1 -1 -1 c b 2 s -1 m 2 d 2 s -1 m -1 f z 1 2 2 4 d 2 s -1 m -1 f -1 2 d 2 s -1 m -1 f Gamma 1 2 h j 2 -1 -1 c b 2 s -1 m 2 d 2 s -1 m -1 f z 1 2 2 4 d 2 s -1 m -1 f -1 -1 -1 c b 2 s -1 m 2 d 2 s -1 m -1 f z 1 2 2 d 2 s -1 m -1 f -1 1 2 d 2 s -1 m -1 f -2 n -2 -1 c b 2 s -1 m 2 4 f d 2 s -1 m -1 g m 2 -1 f d 2 s -1 m -2 n -2 h 0 j j 0 n -1 j -1 h 4 j c b 2 s -1 m -1 h -1 j 2 n c b 2 s -1 m 2 f d 2 s -1 m z 1 2 h j -1 c b 2 s -1 m 2 f d 2 s -1 m z 1 2 2 f d 2 s -1 m -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c b 2 s -1 m c b 2 s -1 m 2 f d 2 s -1 m z 1 2 Gamma 1 2 h j 1 -1 c b 2 s -1 m 2 f d 2 s -1 m z 1 2 2 4 f d 2 s -1 m -1 2 -1 c b 2 s -1 m 2 f d 2 s -1 m z 1 2 2 f d 2 s -1 m -1 1 2 f d 2 s -1 m Gamma 1 2 h j 2 -1 c b 2 s -1 m 2 f d 2 s -1 m z 1 2 2 4 f d 2 s -1 m -1 -1 b m -1 2 s -1 c 2 4 d m -1 2 s -1 f -1 -1 g -1 m 2 -1 d m -1 2 s -1 f -2 n -2 h 0 j j 0 n -1 j -1 h 4 j b m -1 2 s -1 c -1 h -1 j 2 n -1 c b m -1 2 s 2 d m -1 2 s -1 f z 1 2 h j -1 -1 c b m -1 2 s 2 d m -1 2 s -1 f z 1 2 2 d m -1 2 s -1 f -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j b m -1 2 s -1 c -1 c b m -1 2 s 2 d m -1 2 s -1 f z 1 2 Gamma 1 2 h j 1 -1 -1 c b m -1 2 s 2 d m -1 2 s -1 f z 1 2 2 4 d m -1 2 s -1 f -1 2 -1 -1 c b m -1 2 s 2 d m -1 2 s -1 f z 1 2 2 d m -1 2 s -1 f -1 1 2 d m -1 2 s -1 f Gamma 1 2 h j 2 -1 -1 c b m -1 2 s 2 d m -1 2 s -1 f z 1 2 2 4 d m -1 2 s -1 f -1 -1 c b m -1 2 s 2 4 f d m -1 2 s -1 g -1 m 2 -1 f d m -1 2 s -2 n -2 h 0 j j 0 n -1 j -1 h 4 j c b m -1 2 s -1 h -1 j 2 n c b m -1 2 s 2 f d m -1 2 s z 1 2 h j -1 c b m -1 2 s 2 f d m -1 2 s z 1 2 2 f d m -1 2 s -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c b m -1 2 s c b m -1 2 s 2 f d m -1 2 s z 1 2 Gamma 1 2 h j 1 -1 c b m -1 2 s 2 f d m -1 2 s z 1 2 2 4 f d m -1 2 s -1 2 -1 c b m -1 2 s 2 f d m -1 2 s z 1 2 2 f d m -1 2 s -1 1 2 f d m -1 2 s Gamma 1 2 h j 2 -1 c b m -1 2 s 2 f d m -1 2 s z 1 2 2 4 f d m -1 2 s -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["Sin", "[", 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_"]], "+", "g_"]], "]"]]]], 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]", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "f"]]], "-", "g"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "j"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "j"]]], " ", SuperscriptBox["4", "j"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "j", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "j"]]], " ", 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", "-", "j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["j", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", 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", "+", "j"]], ")"]]]], ",", 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"]], " 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18