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/01.20.21.4927.01

 Input Form

 Integrate[z^n E^(b z^2 + d z + e) Sin[a z^2 + p z + q] Sinh[w z^2 + s z + t] Cosh[c z^2 + f z + g]^v, z] == (-I) 2^(-3 - v) Binomial[v, v/2] (1 - Mod[v, 2]) ((-E^(e - I q - t - (d - I p - s)^2/(4 ((-I) a + b - w)))) ((-I) a + b - w)^(-1 - n) Sum[2^(i - n) (-d + I p + s)^(-i + n) (d - I p - s + 2 ((-I) a + b - w) z)^(1 + i) (-((d - I p - s + 2 ((-I) a + b - w) z)^2/((-I) a + b - w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d - I p - s + 2 ((-I) a + b - w) z)^2/(4 ((-I) a + b - w)))], {i, 0, n}] + E^(e + I q - t - (d + I p - s)^2/(4 (I a + b - w))) (I a + b - w)^(-1 - n) Sum[2^(i - n) (-d - I p + s)^(-i + n) (d + I p - s + 2 (I a + b - w) z)^(1 + i) (-((d + I p - s + 2 (I a + b - w) z)^2/(I a + b - w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d + I p - s + 2 (I a + b - w) z)^2/(4 (I a + b - w)))], {i, 0, n}] + E^(e - I q + t - (d - I p + s)^2/(4 ((-I) a + b + w))) ((-I) a + b + w)^(-1 - n) Sum[2^(i - n) (-d + I p - s)^(-i + n) (d - I p + s + 2 ((-I) a + b + w) z)^(1 + i) (-((d - I p + s + 2 ((-I) a + b + w) z)^2/((-I) a + b + w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d - I p + s + 2 ((-I) a + b + w) z)^2/(4 ((-I) a + b + w)))], {i, 0, n}] - E^(e + I q + t - (d + I p + s)^2/(4 (I a + b + w))) (I a + b + w)^(-1 - n) Sum[2^(i - n) (-d - I p - s)^(-i + n) (d + I p + s + 2 (I a + b + w) z)^(1 + i) (-((d + I p + s + 2 (I a + b + w) z)^2/(I a + b + w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d + I p + s + 2 (I a + b + w) z)^2/(4 (I a + b + w)))], {i, 0, n}]) - I 2^(-3 - v) Sum[Binomial[v, h] ((-E^(e - I q - t + g (2 h - v) - (d - I p - s + f (2 h - v))^2/ (4 ((-I) a + b + c (2 h - v) - w)))) ((-I) a + b + c (2 h - v) - w)^(-1 - n) Sum[2^(i - n) (-d + I p + s - f (2 h - v))^(-i + n) (d - I p - s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) - w) z)^ (1 + i) (-((d - I p - s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) - w) z)^2/((-I) a + b + c (2 h - v) - w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d - I p - s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) - w) z)^ 2/(4 ((-I) a + b + c (2 h - v) - w)))], {i, 0, n}] + E^(e + I q - t + g (2 h - v) - (d + I p - s + f (2 h - v))^2/ (4 (I a + b + c (2 h - v) - w))) (I a + b + c (2 h - v) - w)^ (-1 - n) Sum[2^(i - n) (-d - I p + s - f (2 h - v))^(-i + n) (d + I p - s + f (2 h - v) + 2 (I a + b + c (2 h - v) - w) z)^ (1 + i) (-((d + I p - s + f (2 h - v) + 2 (I a + b + c (2 h - v) - w) z)^2/(I a + b + c (2 h - v) - w)))^((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d + I p - s + f (2 h - v) + 2 (I a + b + c (2 h - v) - w) z)^2/ (4 (I a + b + c (2 h - v) - w)))], {i, 0, n}] - E^(e - I q - t + g (-2 h + v) - (d - I p - s + f (-2 h + v))^2/ (4 ((-I) a + b + c (-2 h + v) - w))) ((-I) a + b + c (-2 h + v) - w)^(-1 - n) Sum[2^(i - n) (-d + I p + s - f (-2 h + v))^(-i + n) (d - I p - s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) - w) z)^ (1 + i) (-((d - I p - s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) - w) z)^2/((-I) a + b + c (-2 h + v) - w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d - I p - s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) - w) z)^2/(4 ((-I) a + b + c (-2 h + v) - w)))], {i, 0, n}] + E^(e + I q - t + g (-2 h + v) - (d + I p - s + f (-2 h + v))^2/ (4 (I a + b + c (-2 h + v) - w))) (I a + b + c (-2 h + v) - w)^ (-1 - n) Sum[2^(i - n) (-d - I p + s - f (-2 h + v))^(-i + n) (d + I p - s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) - w) z)^ (1 + i) (-((d + I p - s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) - w) z)^2/(I a + b + c (-2 h + v) - w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d + I p - s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) - w) z)^ 2/(4 (I a + b + c (-2 h + v) - w)))], {i, 0, n}] + E^(e - I q + t + g (2 h - v) - (d - I p + s + f (2 h - v))^2/ (4 ((-I) a + b + c (2 h - v) + w))) ((-I) a + b + c (2 h - v) + w)^ (-1 - n) Sum[2^(i - n) (-d + I p - s - f (2 h - v))^(-i + n) (d - I p + s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) + w) z)^ (1 + i) (-((d - I p + s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) + w) z)^2/((-I) a + b + c (2 h - v) + w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d - I p + s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) + w) z)^ 2/(4 ((-I) a + b + c (2 h - v) + w)))], {i, 0, n}] - E^(e + I q + t + g (2 h - v) - (d + I p + s + f (2 h - v))^2/ (4 (I a + b + c (2 h - v) + w))) (I a + b + c (2 h - v) + w)^ (-1 - n) Sum[2^(i - n) (-d - I p - s - f (2 h - v))^(-i + n) (d + I p + s + f (2 h - v) + 2 (I a + b + c (2 h - v) + w) z)^ (1 + i) (-((d + I p + s + f (2 h - v) + 2 (I a + b + c (2 h - v) + w) z)^2/(I a + b + c (2 h - v) + w)))^((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d + I p + s + f (2 h - v) + 2 (I a + b + c (2 h - v) + w) z)^2/ (4 (I a + b + c (2 h - v) + w)))], {i, 0, n}] + E^(e - I q + t + g (-2 h + v) - (d - I p + s + f (-2 h + v))^2/ (4 ((-I) a + b + c (-2 h + v) + w))) ((-I) a + b + c (-2 h + v) + w)^(-1 - n) Sum[2^(i - n) (-d + I p - s - f (-2 h + v))^(-i + n) (d - I p + s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) + w) z)^ (1 + i) (-((d - I p + s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) + w) z)^2/((-I) a + b + c (-2 h + v) + w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d - I p + s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) + w) z)^2/(4 ((-I) a + b + c (-2 h + v) + w)))], {i, 0, n}] - E^(e + I q + t + g (-2 h + v) - (d + I p + s + f (-2 h + v))^2/ (4 (I a + b + c (-2 h + v) + w))) (I a + b + c (-2 h + v) + w)^ (-1 - n) Sum[2^(i - n) (-d - I p - s - f (-2 h + v))^(-i + n) (d + I p + s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) + w) z)^ (1 + i) (-((d + I p + s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) + w) z)^2/(I a + b + c (-2 h + v) + w)))^ ((1/2) (-1 - i)) Binomial[n, i] Gamma[(1 + i)/2, -((d + I p + s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) + w) z)^ 2/(4 (I a + b + c (-2 h + v) + w)))], {i, 0, n}]), {h, 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 b z 2 + d z + e sin ( a z 2 + p z + q ) sinh ( w z 2 + s z + t ) cosh v ( c z 2 + f z + g ) z - 2 - v - 3 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 1 - v mod 2 \$CellContext`v 2 ) ( - - ( d - p - s ) 2 4 ( b - a - w ) + e - q - t ( i = 0 n 2 i - n ( - d + p + s ) n - i ( d - p - s + 2 ( b - a - w ) z ) i + 1 ( - ( d - p - s + 2 ( b - a - w ) z ) 2 b - a - w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d - p - s + 2 ( b - a - w ) z ) 2 4 ( b - a - w ) ) ) ( b - a - w ) - n - 1 + - ( d + p - s ) 2 4 ( b + a - w ) + e + q - t ( b + a - w ) - n - 1 i = 0 n 2 i - n ( - d - p + s ) n - i ( d + p - s + 2 ( b + a - w ) z ) i + 1 ( - ( d + p - s + 2 ( b + a - w ) z ) 2 b + a - w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d + p - s + 2 ( b + a - w ) z ) 2 4 ( b + a - w ) ) + - ( d - p + s ) 2 4 ( b - a + w ) + e - q + t ( b - a + w ) - n - 1 i = 0 n 2 i - n ( - d + p - s ) n - i ( d - p + s + 2 ( b - a + w ) z ) i + 1 ( - ( d - p + s + 2 ( b - a + w ) z ) 2 b - a + w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d - p + s + 2 ( b - a + w ) z ) 2 4 ( b - a + w ) ) - - ( d + p + s ) 2 4 ( b + a + w ) + e + q + t ( b + a + w ) - n - 1 i = 0 n 2 i - n ( - d - p - s ) n - i ( d + p + s + 2 ( b + a + w ) z ) i + 1 ( - ( d + p + s + 2 ( b + a + w ) z ) 2 b + a + w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d + p + s + 2 ( b + a + w ) z ) 2 4 ( b + a + w ) ) ) - 2 - v - 3 h = 0 v - 1 2 ( v h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["h", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - - ( d - p - s + f ( 2 h - v ) ) 2 4 ( b - a + c ( 2 h - v ) - w ) + e - q - t + g ( 2 h - v ) ( i = 0 n 2 i - n ( - d + p + s - f ( 2 h - v ) ) n - i ( d - p - s + f ( 2 h - v ) + 2 ( b - a + c ( 2 h - v ) - w ) z ) i + 1 ( - ( d - p - s + f ( 2 h - v ) + 2 ( b - a + c ( 2 h - v ) - w ) z ) 2 b - a + c ( 2 h - v ) - w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d - p - s + f ( 2 h - v ) + 2 ( b - a + c ( 2 h - v ) - w ) z ) 2 4 ( b - a + c ( 2 h - v ) - w ) ) ) ( b - a + c ( 2 h - v ) - w ) - n - 1 + - ( d + p - s + f ( 2 h - v ) ) 2 4 ( b + a + c ( 2 h - v ) - w ) + e + q - t + g ( 2 h - v ) ( b + a + c ( 2 h - v ) - w ) - n - 1 i = 0 n 2 i - n ( - d - p + s - f ( 2 h - v ) ) n - i ( d + p - s + f ( 2 h - v ) + 2 ( b + a + c ( 2 h - v ) - w ) z ) i + 1 ( - ( d + p - s + f ( 2 h - v ) + 2 ( b + a + c ( 2 h - v ) - w ) z ) 2 b + a + c ( 2 h - v ) - w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d + p - s + f ( 2 h - v ) + 2 ( b + a + c ( 2 h - v ) - w ) z ) 2 4 ( b + a + c ( 2 h - v ) - w ) ) - - ( d - p - s + f ( v - 2 h ) ) 2 4 ( b - a + c ( v - 2 h ) - w ) + e - q - t + g ( v - 2 h ) ( b - a + c ( v - 2 h ) - w ) - n - 1 i = 0 n 2 i - n ( - d + p + s - f ( v - 2 h ) ) n - i ( d - p - s + f ( v - 2 h ) + 2 ( b - a + c ( v - 2 h ) - w ) z ) i + 1 ( - ( d - p - s + f ( v - 2 h ) + 2 ( b - a + c ( v - 2 h ) - w ) z ) 2 b - a + c ( v - 2 h ) - w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d - p - s + f ( v - 2 h ) + 2 ( b - a + c ( v - 2 h ) - w ) z ) 2 4 ( b - a + c ( v - 2 h ) - w ) ) + - ( d + p - s + f ( v - 2 h ) ) 2 4 ( b + a + c ( v - 2 h ) - w ) + e + q - t + g ( v - 2 h ) ( b + a + c ( v - 2 h ) - w ) - n - 1 i = 0 n 2 i - n ( - d - p + s - f ( v - 2 h ) ) n - i ( d + p - s + f ( v - 2 h ) + 2 ( b + a + c ( v - 2 h ) - w ) z ) i + 1 ( - ( d + p - s + f ( v - 2 h ) + 2 ( b + a + c ( v - 2 h ) - w ) z ) 2 b + a + c ( v - 2 h ) - w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d + p - s + f ( v - 2 h ) + 2 ( b + a + c ( v - 2 h ) - w ) z ) 2 4 ( b + a + c ( v - 2 h ) - w ) ) + - ( d - p + s + f ( 2 h - v ) ) 2 4 ( b - a + c ( 2 h - v ) + w ) + e - q + t + g ( 2 h - v ) ( b - a + c ( 2 h - v ) + w ) - n - 1 i = 0 n 2 i - n ( - d + p - s - f ( 2 h - v ) ) n - i ( d - p + s + f ( 2 h - v ) + 2 ( b - a + c ( 2 h - v ) + w ) z ) i + 1 ( - ( d - p + s + f ( 2 h - v ) + 2 ( b - a + c ( 2 h - v ) + w ) z ) 2 b - a + c ( 2 h - v ) + w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d - p + s + f ( 2 h - v ) + 2 ( b - a + c ( 2 h - v ) + w ) z ) 2 4 ( b - a + c ( 2 h - v ) + w ) ) - - ( d + p + s + f ( 2 h - v ) ) 2 4 ( b + a + c ( 2 h - v ) + w ) + e + q + t + g ( 2 h - v ) ( b + a + c ( 2 h - v ) + w ) - n - 1 i = 0 n 2 i - n ( - d - p - s - f ( 2 h - v ) ) n - i ( d + p + s + f ( 2 h - v ) + 2 ( b + a + c ( 2 h - v ) + w ) z ) i + 1 ( - ( d + p + s + f ( 2 h - v ) + 2 ( b + a + c ( 2 h - v ) + w ) z ) 2 b + a + c ( 2 h - v ) + w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d + p + s + f ( 2 h - v ) + 2 ( b + a + c ( 2 h - v ) + w ) z ) 2 4 ( b + a + c ( 2 h - v ) + w ) ) + - ( d - p + s + f ( v - 2 h ) ) 2 4 ( b - a + c ( v - 2 h ) + w ) + e - q + t + g ( v - 2 h ) ( b - a + c ( v - 2 h ) + w ) - n - 1 i = 0 n 2 i - n ( - d + p - s - f ( v - 2 h ) ) n - i ( d - p + s + f ( v - 2 h ) + 2 ( b - a + c ( v - 2 h ) + w ) z ) i + 1 ( - ( d - p + s + f ( v - 2 h ) + 2 ( b - a + c ( v - 2 h ) + w ) z ) 2 b - a + c ( v - 2 h ) + w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d - p + s + f ( v - 2 h ) + 2 ( b - a + c ( v - 2 h ) + w ) z ) 2 4 ( b - a + c ( v - 2 h ) + w ) ) - - ( d + p + s + f ( v - 2 h ) ) 2 4 ( b + a + c ( v - 2 h ) + w ) + e + q + t + g ( v - 2 h ) ( b + a + c ( v - 2 h ) + w ) - n - 1 i = 0 n 2 i - n ( - d - p - s - f ( v - 2 h ) ) n - i ( d + p + s + f ( v - 2 h ) + 2 ( b + a + c ( v - 2 h ) + w ) z ) i + 1 ( - ( d + p + s + f ( v - 2 h ) + 2 ( b + a + c ( v - 2 h ) + w ) z ) 2 b + a + c ( v - 2 h ) + w ) 1 2 ( - i - 1 ) ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["i", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( i + 1 2 , - ( d + p + s + f ( v - 2 h ) + 2 ( b + a + c ( v - 2 h ) + w ) z ) 2 4 ( b + a + c ( v - 2 h ) + w ) ) ) /; n v + Condition z z n b z 2 d z e a z 2 p z q w z 2 s z t c z 2 f z g v -1 2 -1 v -3 Binomial v v 2 -1 1 -1 \$CellContext`v 2 -1 -1 d -1 p -1 s 2 4 b -1 a -1 w -1 e -1 q -1 t i 0 n 2 i -1 n -1 d p s n -1 i d -1 p -1 s 2 b -1 a -1 w z i 1 -1 d -1 p -1 s 2 b -1 a -1 w z 2 b -1 a -1 w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d -1 p -1 s 2 b -1 a -1 w z 2 4 b -1 a -1 w -1 b -1 a -1 w -1 n -1 -1 d p -1 s 2 4 b a -1 w -1 e q -1 t b a -1 w -1 n -1 i 0 n 2 i -1 n -1 d -1 p s n -1 i d p -1 s 2 b a -1 w z i 1 -1 d p -1 s 2 b a -1 w z 2 b a -1 w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d p -1 s 2 b a -1 w z 2 4 b a -1 w -1 -1 d -1 p s 2 4 b -1 a w -1 e -1 q t b -1 a w -1 n -1 i 0 n 2 i -1 n -1 d p -1 s n -1 i d -1 p s 2 b -1 a w z i 1 -1 d -1 p s 2 b -1 a w z 2 b -1 a w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d -1 p s 2 b -1 a w z 2 4 b -1 a w -1 -1 -1 d p s 2 4 b a w -1 e q t b a w -1 n -1 i 0 n 2 i -1 n -1 d -1 p -1 s n -1 i d p s 2 b a w z i 1 -1 d p s 2 b a w z 2 b a w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d p s 2 b a w z 2 4 b a w -1 -1 2 -1 v -3 h 0 v -1 2 -1 Binomial v h -1 -1 d -1 p -1 s f 2 h -1 v 2 4 b -1 a c 2 h -1 v -1 w -1 e -1 q -1 t g 2 h -1 v i 0 n 2 i -1 n -1 d p s -1 f 2 h -1 v n -1 i d -1 p -1 s f 2 h -1 v 2 b -1 a c 2 h -1 v -1 w z i 1 -1 d -1 p -1 s f 2 h -1 v 2 b -1 a c 2 h -1 v -1 w z 2 b -1 a c 2 h -1 v -1 w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d -1 p -1 s f 2 h -1 v 2 b -1 a c 2 h -1 v -1 w z 2 4 b -1 a c 2 h -1 v -1 w -1 b -1 a c 2 h -1 v -1 w -1 n -1 -1 d p -1 s f 2 h -1 v 2 4 b a c 2 h -1 v -1 w -1 e q -1 t g 2 h -1 v b a c 2 h -1 v -1 w -1 n -1 i 0 n 2 i -1 n -1 d -1 p s -1 f 2 h -1 v n -1 i d p -1 s f 2 h -1 v 2 b a c 2 h -1 v -1 w z i 1 -1 d p -1 s f 2 h -1 v 2 b a c 2 h -1 v -1 w z 2 b a c 2 h -1 v -1 w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d p -1 s f 2 h -1 v 2 b a c 2 h -1 v -1 w z 2 4 b a c 2 h -1 v -1 w -1 -1 -1 d -1 p -1 s f v -1 2 h 2 4 b -1 a c v -1 2 h -1 w -1 e -1 q -1 t g v -1 2 h b -1 a c v -1 2 h -1 w -1 n -1 i 0 n 2 i -1 n -1 d p s -1 f v -1 2 h n -1 i d -1 p -1 s f v -1 2 h 2 b -1 a c v -1 2 h -1 w z i 1 -1 d -1 p -1 s f v -1 2 h 2 b -1 a c v -1 2 h -1 w z 2 b -1 a c v -1 2 h -1 w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d -1 p -1 s f v -1 2 h 2 b -1 a c v -1 2 h -1 w z 2 4 b -1 a c v -1 2 h -1 w -1 -1 d p -1 s f v -1 2 h 2 4 b a c v -1 2 h -1 w -1 e q -1 t g v -1 2 h b a c v -1 2 h -1 w -1 n -1 i 0 n 2 i -1 n -1 d -1 p s -1 f v -1 2 h n -1 i d p -1 s f v -1 2 h 2 b a c v -1 2 h -1 w z i 1 -1 d p -1 s f v -1 2 h 2 b a c v -1 2 h -1 w z 2 b a c v -1 2 h -1 w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d p -1 s f v -1 2 h 2 b a c v -1 2 h -1 w z 2 4 b a c v -1 2 h -1 w -1 -1 d -1 p s f 2 h -1 v 2 4 b -1 a c 2 h -1 v w -1 e -1 q t g 2 h -1 v b -1 a c 2 h -1 v w -1 n -1 i 0 n 2 i -1 n -1 d p -1 s -1 f 2 h -1 v n -1 i d -1 p s f 2 h -1 v 2 b -1 a c 2 h -1 v w z i 1 -1 d -1 p s f 2 h -1 v 2 b -1 a c 2 h -1 v w z 2 b -1 a c 2 h -1 v w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d -1 p s f 2 h -1 v 2 b -1 a c 2 h -1 v w z 2 4 b -1 a c 2 h -1 v w -1 -1 -1 d p s f 2 h -1 v 2 4 b a c 2 h -1 v w -1 e q t g 2 h -1 v b a c 2 h -1 v w -1 n -1 i 0 n 2 i -1 n -1 d -1 p -1 s -1 f 2 h -1 v n -1 i d p s f 2 h -1 v 2 b a c 2 h -1 v w z i 1 -1 d p s f 2 h -1 v 2 b a c 2 h -1 v w z 2 b a c 2 h -1 v w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d p s f 2 h -1 v 2 b a c 2 h -1 v w z 2 4 b a c 2 h -1 v w -1 -1 d -1 p s f v -1 2 h 2 4 b -1 a c v -1 2 h w -1 e -1 q t g v -1 2 h b -1 a c v -1 2 h w -1 n -1 i 0 n 2 i -1 n -1 d p -1 s -1 f v -1 2 h n -1 i d -1 p s f v -1 2 h 2 b -1 a c v -1 2 h w z i 1 -1 d -1 p s f v -1 2 h 2 b -1 a c v -1 2 h w z 2 b -1 a c v -1 2 h w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d -1 p s f v -1 2 h 2 b -1 a c v -1 2 h w z 2 4 b -1 a c v -1 2 h w -1 -1 -1 d p s f v -1 2 h 2 4 b a c v -1 2 h w -1 e q t g v -1 2 h b a c v -1 2 h w -1 n -1 i 0 n 2 i -1 n -1 d -1 p -1 s -1 f v -1 2 h n -1 i d p s f v -1 2 h 2 b a c v -1 2 h w z i 1 -1 d p s f v -1 2 h 2 b a c v -1 2 h w z 2 b a c v -1 2 h w -1 1 2 -1 i -1 Binomial n i Gamma i 1 2 -1 -1 d p s f v -1 2 h 2 b a c v -1 2 h w z 2 4 b a c v -1 2 h w -1 n v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["w_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["s_", " ", "z_"]], "+", "t_"]], "]"]], " ", 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[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", RowBox[List["\[ImaginaryI]", " ", "q"]], "-", "t", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "w"]], ")"]]]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "w"]], ")"]], RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[SuperscriptBox["2", RowBox[List["i", "-", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", "s"]], ")"]], RowBox[List[RowBox[List["-", "i"]], "+", "n"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "w"]], ")"]], " ", "z"]]]], ")"]], RowBox[List["1", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]], "-", "s", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "w"]], ")"]], " ", "z"]]]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b", "-", "w"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18