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http://functions.wolfram.com/01.07.21.2477.01
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Integrate[z^n Sin[b z^2 + d z] Cos[c z^2 + f z]^v, z] ==
2^(-2 - v) (((-I) ((-I) b)^(-1 - n) Binomial[v, v/2] (-1 + Mod[v, 2])
(Sum[2^(-n + q) (I d)^(n - q) ((-I) (d + 2 b z))^(1 + q)
(-((I (d + 2 b z)^2)/b))^((1/2) (-1 - q)) Binomial[n, q]
Gamma[(1 + q)/2, -((I (d + 2 b z)^2)/(4 b))], {q, 0, n}] -
E^((I d^2)/(2 b)) Sum[2^(-n + q) (I d)^(n - q) ((-I) (d + 2 b z))^
(1 + q) ((I (d + 2 b z)^2)/b)^((1/2) (-1 - q)) Binomial[n, q]
Gamma[(1 + q)/2, (I (d + 2 b z)^2)/(4 b)], {q, 0, n}]))/
E^((I d^2)/(4 b)) +
I Sum[Binomial[v, s]
(E^(I (Pi - (-d - 2 f s + f v)^2/(-4 b - 8 c s + 4 c v)))
(I (-b - 2 c s + c v))^(-1 - n)
Sum[2^(-n + q) ((-I) (-d - 2 f s + f v))^(n - q)
(I (-d + f (-2 s + v) + 2 (-b - 2 c s + c v) z))^(1 + q)
(-((I (-d + f (-2 s + v) + 2 (-b - 2 c s + c v) z)^2)/
(-b - 2 c s + c v)))^((1/2) (-1 - q)) Binomial[n, q]
Gamma[(1 + q)/2, -((I (-d + f (-2 s + v) + 2 (-b - 2 c s + c v) z)^
2)/(-4 b - 8 c s + 4 c v))], {q, 0, n}] +
E^((I (-d - 2 f s + f v)^2)/(-4 b - 8 c s + 4 c v))
((-I) (-b - 2 c s + c v))^(-1 - n)
Sum[2^(-n + q) (I (-d - 2 f s + f v))^(n - q)
((-I) (-d + f (-2 s + v) + 2 (-b - 2 c s + c v) z))^(1 + q)
((I (-d + f (-2 s + v) + 2 (-b - 2 c s + c v) z)^2)/
(-b - 2 c s + c v))^((1/2) (-1 - q)) Binomial[n, q]
Gamma[(1 + q)/2, (I (-d + f (-2 s + v) + 2 (-b - 2 c s + c v) z)^
2)/(-4 b - 8 c s + 4 c v)], {q, 0, n}] +
E^(I (Pi - (d + f (-2 s + v))^2/(-4 b + 8 c s - 4 c v)))
(I (-b + 2 c s - c v))^(-1 - n)
Sum[2^(-n + q) ((-I) (-d + 2 f s - f v))^(n - q)
(I (-d + 2 f s - f v - 2 b z + 4 c s z - 2 c v z))^(1 + q)
(-((I (d + f (-2 s + v) + 2 (b - 2 c s + c v) z)^2)/
(-b + 2 c s - c v)))^((1/2) (-1 - q)) Binomial[n, q]
Gamma[(1 + q)/2, -((I (d + f (-2 s + v) + 2 (b - 2 c s + c v) z)^
2)/(-4 b + 8 c s - 4 c v))], {q, 0, n}] +
E^((I (d + f (-2 s + v))^2)/(-4 b + 8 c s - 4 c v))
((-I) (-b + 2 c s - c v))^(-1 - n)
Sum[2^(-n + q) (I (-d + 2 f s - f v))^(n - q)
((-I) (-d + 2 f s - f v - 2 b z + 4 c s z - 2 c v z))^(1 + q)
((I (d + f (-2 s + v) + 2 (b - 2 c s + c v) z)^2)/
(-b + 2 c s - c v))^((1/2) (-1 - q)) Binomial[n, q]
Gamma[(1 + q)/2, (I (d + f (-2 s + v) + 2 (b - 2 c s + c v) z)^2)/
(-4 b + 8 c s - 4 c v)], {q, 0, n}]),
{s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[n, Integers] && n >= 0 &&
Element[v, Integers] && v > 0
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ∫ </mo> <mrow> <msup> <mi> z </mi> <mi> n </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mi> v </mi> </msup> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> v </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> s </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> v </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mi> s </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> π </mi> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> π </mi> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> d </mi> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> v </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> v </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> v </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> d </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mi> b </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mi> d </mi> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> q </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> d </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mi> b </mi> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> q </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> <mo> ∧ </mo> <mrow> <mi> v </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <sin /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <cos /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <sum /> <bvar> <ci> s </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> f </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> f </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> f </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> f </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> f </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> f </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> f </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn 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<apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> q </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> ℕ </ci> </apply> <apply> <in /> <ci> v </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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