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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and a power functions > Involving powers of sin and power > Involving zn sinm(b zr+d z) cos(c zr+g)





http://functions.wolfram.com/01.07.21.0872.01









  


  










Input Form





Integrate[z^n Sin[b z^2 + d z]^m Cos[c z^2 + g], z] == 2^(-2 - m) ((-E^(I g)) z^(1 + n) (c^2 z^4)^((1/2) (-1 - n)) Binomial[m, m/2] ((I c z^2)^((1 + n)/2) Gamma[(1 + n)/2, (-I) c z^2] + (((-I) c z^2)^((1 + n)/2) Gamma[(1 + n)/2, I c z^2])/E^(2 I g)) (1 - Mod[m, 2]) - (E^(I g) Sum[(-1)^k Binomial[m, k] (E^(I (-((2 d k - d m)^2/(4 c + 8 b k - 4 b m)) + m Pi)) (I (c + 2 b k - b m))^(-1 - n) Sum[2^(-n + q) ((-I) (2 d k - d m))^ (n - q) (I (d (2 k - m) + 2 (c + 2 b k - b m) z))^(1 + q) (-((I (d (2 k - m) + 2 (c + 2 b k - b m) z)^2)/(c + 2 b k - b m)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I (d (2 k - m) + 2 (c + 2 b k - b m) z)^2)/(4 c + 8 b k - 4 b m))], {q, 0, n}] + E^(-2 I g + (I (2 d k - d m)^2)/(4 c + 8 b k - 4 b m)) ((-I) (c + 2 b k - b m))^(-1 - n) Sum[2^(-n + q) (I (2 d k - d m))^(n - q) ((-I) (d (2 k - m) + 2 (c + 2 b k - b m) z))^(1 + q) ((I (d (2 k - m) + 2 (c + 2 b k - b m) z)^2)/(c + 2 b k - b m))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (d (2 k - m) + 2 (c + 2 b k - b m) z)^2)/(4 c + 8 b k - 4 b m)], {q, 0, n}] + E^(I (-2 g - (d^2 (-2 k + m)^2)/(-4 c + 8 b k - 4 b m) + m Pi)) (I (-c + 2 b k - b m))^(-1 - n) Sum[2^(-n + q) ((-I) (2 d k - d m))^ (n - q) (I (2 d k - d m - 2 c z + 4 b k z - 2 b m z))^(1 + q) (-((I (d (-2 k + m) + 2 (c - 2 b k + b m) z)^2)/(-c + 2 b k - b m)))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I (d (-2 k + m) + 2 (c - 2 b k + b m) z)^2)/(-4 c + 8 b k - 4 b m))], {q, 0, n}] + E^((I d^2 (-2 k + m)^2)/ (-4 c + 8 b k - 4 b m)) ((-I) (-c + 2 b k - b m))^(-1 - n) Sum[2^(-n + q) (I (2 d k - d m))^(n - q) ((-I) (2 d k - d m - 2 c z + 4 b k z - 2 b m z))^(1 + q) ((I (d (-2 k + m) + 2 (c - 2 b k + b m) z)^2)/(-c + 2 b k - b m))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (I (d (-2 k + m) + 2 (c - 2 b k + b m) z)^2)/(-4 c + 8 b k - 4 b m)], {q, 0, n}]), {k, 0, Floor[(1/2) (-1 + m)]}])/I^m) /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> z </mi> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mi> m </mi> </msup> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mi> g </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> g </mi> </mrow> </msup> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[FractionBox[&quot;m&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> g </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> &#8520; </mi> <mrow> <mo> - </mo> <mi> m </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> g </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[&quot;k&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8721; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </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[&quot;(&quot;, GridBox[List[List[TagBox[&quot;n&quot;, Identity]], List[TagBox[&quot;q&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </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> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> d </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> g </mi> </mrow> <mo> + </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </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> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </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[&quot;(&quot;, GridBox[List[List[TagBox[&quot;n&quot;, Identity]], List[TagBox[&quot;q&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </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> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> g </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </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> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </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[&quot;(&quot;, GridBox[List[List[TagBox[&quot;n&quot;, Identity]], List[TagBox[&quot;q&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </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> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mi> q </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </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> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> q </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </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[&quot;(&quot;, GridBox[List[List[TagBox[&quot;n&quot;, Identity]], List[TagBox[&quot;q&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </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> &#8520; </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </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> <power /> <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> <ci> m </ci> </apply> <apply> <cos /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> g </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> 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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'> 2 </cn> <ci> d </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> d </ci> <ci> m </ci> </apply> </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'> 2 </cn> <ci> d </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> z </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> d </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> m </ci> <ci> z </ci> </apply> </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 /> <ci> d </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <ci> m </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> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </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 /> <ci> d </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <ci> m </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> c </ci> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> d </ci> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </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 /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> d </ci> <ci> m </ci> </apply> </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 /> <ci> d </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </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 /> <ci> d </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </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> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18