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 Cosh

 http://functions.wolfram.com/01.20.21.3722.01

 Input Form

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

 Standard Form

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"j"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", 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 MathML Form

 z n cos m ( b z 2 + d z ) cosh v ( c z 2 + f z + g ) z ( 2 - m - v 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) n + 1 - 2 - m - v - 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 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( 2 k - m ) d 2 4 b ( j = 0 n 2 j - n ( - d ( 2 k - m ) ) n - j ( d ( 2 k - m ) + 2 b z ( 2 k - m ) ) j + 1 ( ( d ( 2 k - m ) + 2 b z ( 2 k - m ) ) 2 b ( 2 k - m ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( d ( 2 k - m ) + 2 b z ( 2 k - m ) ) 2 4 b ( 2 k - m ) ) ) ( b ( 2 k - m ) ) - n - 1 + - ( m - 2 k ) d 2 4 b ( b ( m - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - d ( m - 2 k ) ) n - j ( d ( m - 2 k ) + 2 b z ( m - 2 k ) ) j + 1 ( ( d ( m - 2 k ) + 2 b z ( m - 2 k ) ) 2 b ( m - 2 k ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( d ( m - 2 k ) + 2 b z ( m - 2 k ) ) 2 4 b ( m - 2 k ) ) ) - 2 - m - v - 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( g ( 2 k - v ) - f 2 ( 2 k - v ) 4 c ( j = 0 n 2 j - n ( - f ( 2 k - v ) ) n - j ( f ( 2 k - v ) + 2 c z ( 2 k - v ) ) j + 1 ( - ( f ( 2 k - v ) + 2 c z ( 2 k - v ) ) 2 c ( 2 k - v ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( f ( 2 k - v ) + 2 c z ( 2 k - v ) ) 2 4 c ( 2 k - v ) ) ) ( c ( 2 k - v ) ) - n - 1 + g ( v - 2 k ) - f 2 ( v - 2 k ) 4 c ( c ( v - 2 k ) ) - n - 1 j = 0 n 2 j - n ( - f ( v - 2 k ) ) n - j ( f ( v - 2 k ) + 2 c z ( v - 2 k ) ) j + 1 ( - ( f ( v - 2 k ) + 2 c z ( v - 2 k ) ) 2 c ( v - 2 k ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( f ( v - 2 k ) + 2 c z ( v - 2 k ) ) 2 4 c ( v - 2 k ) ) ) - 2 - m - v - 1 k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[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]]]]] ( - ( d ( 2 k - m ) + f ( 2 s - v ) ) 2 4 ( b ( 2 k - m ) + c ( 2 s - v ) ) + g ( 2 s - v ) ( j = 0 n 2 j - n ( - d ( 2 k - m ) - f ( 2 s - v ) ) n - j ( d ( 2 k - m ) + f ( 2 s - v ) + 2 ( b ( 2 k - m ) + c ( 2 s - v ) ) z ) j + 1 ( - ( d ( 2 k - m ) + f ( 2 s - v ) + 2 ( b ( 2 k - m ) + c ( 2 s - v ) ) z ) 2 / ( b ( 2 k - m ) + c ( 2 s - v ) ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d ( 2 k - m ) + f ( 2 s - v ) + 2 ( b ( 2 k - m ) + c ( 2 s - v ) ) z ) 2 4 ( b ( 2 k - m ) + c ( 2 s - v ) ) ) ) ( b ( 2 k - m ) + c ( 2 s - v ) ) - n - 1 + - ( d ( m - 2 k ) + f ( 2 s - v ) ) 2 4 ( b ( m - 2 k ) + c ( 2 s - v ) ) + g ( 2 s - v ) ( b ( m - 2 k ) + c ( 2 s - v ) ) - n - 1 j = 0 n 2 j - n ( - d ( m - 2 k ) - f ( 2 s - v ) ) n - j ( d ( m - 2 k ) + f ( 2 s - v ) + 2 ( b ( m - 2 k ) + c ( 2 s - v ) ) z ) j + 1 ( - ( d ( m - 2 k ) + f ( 2 s - v ) + 2 ( b ( m - 2 k ) + c ( 2 s - v ) ) z ) 2 b ( m - 2 k ) + c ( 2 s - v ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d ( m - 2 k ) + f ( 2 s - v ) + 2 ( b ( m - 2 k ) + c ( 2 s - v ) ) z ) 2 4 ( b ( m - 2 k ) + c ( 2 s - v ) ) ) + - ( d ( 2 k - m ) + f ( v - 2 s ) ) 2 4 ( b ( 2 k - m ) + c ( v - 2 s ) ) + g ( v - 2 s ) ( b ( 2 k - m ) + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d ( 2 k - m ) - f ( v - 2 s ) ) n - j ( d ( 2 k - m ) + f ( v - 2 s ) + 2 ( b ( 2 k - m ) + c ( v - 2 s ) ) z ) j + 1 ( - ( d ( 2 k - m ) + f ( v - 2 s ) + 2 ( b ( 2 k - m ) + c ( v - 2 s ) ) z ) 2 b ( 2 k - m ) + c ( v - 2 s ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d ( 2 k - m ) + f ( v - 2 s ) + 2 ( b ( 2 k - m ) + c ( v - 2 s ) ) z ) 2 4 ( b ( 2 k - m ) + c ( v - 2 s ) ) ) + - ( d ( m - 2 k ) + f ( v - 2 s ) ) 2 4 ( b ( m - 2 k ) + c ( v - 2 s ) ) + g ( v - 2 s ) ( b ( m - 2 k ) + c ( v - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - d ( m - 2 k ) - f ( v - 2 s ) ) n - j ( d ( m - 2 k ) + f ( v - 2 s ) + 2 ( b ( m - 2 k ) + c ( v - 2 s ) ) z ) j + 1 ( - ( d ( m - 2 k ) + f ( v - 2 s ) + 2 ( b ( m - 2 k ) + c ( v - 2 s ) ) z ) 2 b ( m - 2 k ) + c ( v - 2 s ) ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d ( m - 2 k ) + f ( v - 2 s ) + 2 ( b ( m - 2 k ) + c ( v - 2 s ) ) z ) 2 4 ( b ( m - 2 k ) + c ( v - 2 s ) ) ) ) /; n m + v + Condition z z n b z 2 d z m c z 2 f z g v 2 -1 m -1 v z n 1 Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 n 1 -1 -1 2 -1 m -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 Binomial m k -1 2 k -1 m d 2 4 b -1 j 0 n 2 j -1 n -1 d 2 k -1 m n -1 j d 2 k -1 m 2 b z 2 k -1 m j 1 d 2 k -1 m 2 b z 2 k -1 m 2 b 2 k -1 m -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 d 2 k -1 m 2 b z 2 k -1 m 2 4 b 2 k -1 m -1 b 2 k -1 m -1 n -1 -1 m -1 2 k d 2 4 b -1 b m -1 2 k -1 n -1 j 0 n 2 j -1 n -1 d m -1 2 k n -1 j d m -1 2 k 2 b z m -1 2 k j 1 d m -1 2 k 2 b z m -1 2 k 2 b m -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 d m -1 2 k 2 b z m -1 2 k 2 4 b m -1 2 k -1 -1 2 -1 m -1 v -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 k 0 v -1 2 -1 Binomial v k g 2 k -1 v -1 f 2 2 k -1 v 4 c -1 j 0 n 2 j -1 n -1 f 2 k -1 v n -1 j f 2 k -1 v 2 c z 2 k -1 v j 1 -1 f 2 k -1 v 2 c z 2 k -1 v 2 c 2 k -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f 2 k -1 v 2 c z 2 k -1 v 2 4 c 2 k -1 v -1 c 2 k -1 v -1 n -1 g v -1 2 k -1 f 2 v -1 2 k 4 c -1 c v -1 2 k -1 n -1 j 0 n 2 j -1 n -1 f v -1 2 k n -1 j f v -1 2 k 2 c z v -1 2 k j 1 -1 f v -1 2 k 2 c z v -1 2 k 2 c v -1 2 k -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f v -1 2 k 2 c z v -1 2 k 2 4 c v -1 2 k -1 -1 2 -1 m -1 v -1 k 0 m -1 2 -1 Binomial m k s 0 v -1 2 -1 Binomial v s -1 d 2 k -1 m f 2 s -1 v 2 4 b 2 k -1 m c 2 s -1 v -1 g 2 s -1 v j 0 n 2 j -1 n -1 d 2 k -1 m -1 f 2 s -1 v n -1 j d 2 k -1 m f 2 s -1 v 2 b 2 k -1 m c 2 s -1 v z j 1 -1 d 2 k -1 m f 2 s -1 v 2 b 2 k -1 m c 2 s -1 v z 2 b 2 k -1 m c 2 s -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 k -1 m f 2 s -1 v 2 b 2 k -1 m c 2 s -1 v z 2 4 b 2 k -1 m c 2 s -1 v -1 b 2 k -1 m c 2 s -1 v -1 n -1 -1 d m -1 2 k f 2 s -1 v 2 4 b m -1 2 k c 2 s -1 v -1 g 2 s -1 v b m -1 2 k c 2 s -1 v -1 n -1 j 0 n 2 j -1 n -1 d m -1 2 k -1 f 2 s -1 v n -1 j d m -1 2 k f 2 s -1 v 2 b m -1 2 k c 2 s -1 v z j 1 -1 d m -1 2 k f 2 s -1 v 2 b m -1 2 k c 2 s -1 v z 2 b m -1 2 k c 2 s -1 v -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k f 2 s -1 v 2 b m -1 2 k c 2 s -1 v z 2 4 b m -1 2 k c 2 s -1 v -1 -1 d 2 k -1 m f v -1 2 s 2 4 b 2 k -1 m c v -1 2 s -1 g v -1 2 s b 2 k -1 m c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d 2 k -1 m -1 f v -1 2 s n -1 j d 2 k -1 m f v -1 2 s 2 b 2 k -1 m c v -1 2 s z j 1 -1 d 2 k -1 m f v -1 2 s 2 b 2 k -1 m c v -1 2 s z 2 b 2 k -1 m c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 k -1 m f v -1 2 s 2 b 2 k -1 m c v -1 2 s z 2 4 b 2 k -1 m c v -1 2 s -1 -1 d m -1 2 k f v -1 2 s 2 4 b m -1 2 k c v -1 2 s -1 g v -1 2 s b m -1 2 k c v -1 2 s -1 n -1 j 0 n 2 j -1 n -1 d m -1 2 k -1 f v -1 2 s n -1 j d m -1 2 k f v -1 2 s 2 b m -1 2 k c v -1 2 s z j 1 -1 d m -1 2 k f v -1 2 s 2 b m -1 2 k c v -1 2 s z 2 b m -1 2 k c v -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k f v -1 2 s 2 b m -1 2 k c v -1 2 s z 2 4 b m -1 2 k c v -1 2 s -1 n m SuperPlus v 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_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]]]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "m"]], "-", "v"]]], " ", SuperscriptBox["z", RowBox[List["n", "+", "1"]]]]], ")"]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18