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MathieuC






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuC[a,q,z] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.01.06.0003.01









  


  










Input Form





MathieuC[MathieuCharacteristicA[r, q], q, z] \[Proportional] Cos[r z] + (1/4) (Cos[(r - 2) z]/(r - 1) - Cos[(r + 2) z]/(r + 1)) q + (1/32) (Cos[(r - 4) z]/((r - 2) (r - 1)) - (2 (r^2 + 1) Cos[r z])/ ((r - 1)^2 (r + 1)^2) + Cos[(r + 4) z]/((r + 1) (r + 2))) q^2 + (1/384) (Cos[(r - 6) z]/((r - 3) (r - 2) (r - 1)) - (3 (r^3 - r^2 - r - 11) Cos[(r - 2) z])/((r - 2) (r - 1)^3 (r + 1)^2) + (3 (r^3 + r^2 - r + 11) Cos[(r + 2) z])/((r - 1)^2 (r + 1)^3 (r + 2)) - Cos[(r + 6) z]/((r + 1) (r + 2) (r + 3))) q^3 + (1/6144) (Cos[(r - 8) z]/((r - 4) (r - 3) (r - 2) (r - 1)) - (4 (r^3 - r^2 - 7 r - 29) Cos[(r - 4) z])/((r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (6 (r^8 - 15 r^6 - 185 r^4 + 675 r^2 + 316) Cos[r z])/ ((r - 2)^2 (r - 1)^4 (r + 1)^4 (r + 2)^2) - (4 (r^3 + r^2 - 7 r + 29) Cos[(r + 4) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3)) + Cos[(r + 8) z]/((r + 1) (r + 2) (r + 3) (r + 4))) q^4 + (1/122880) (Cos[(r - 10) z]/((r - 5) (r - 4) (r - 3) (r - 2) (r - 1)) - (5 (r^3 - r^2 - 17 r - 55) Cos[(r - 6) z])/((r - 4) (r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (10 (r^9 - r^8 - 31 r^7 - 5 r^6 - 273 r^5 + 2457 r^4 + 1931 r^3 - 6335 r^2 - 3572 r - 7564) Cos[(r - 2) z])/ ((r - 3) (r - 2)^2 (r - 1)^5 (r + 1)^4 (r + 2)^2) - (10 (r^9 + r^8 - 31 r^7 + 5 r^6 - 273 r^5 - 2457 r^4 + 1931 r^3 + 6335 r^2 - 3572 r + 7564) Cos[(r + 2) z])/((r - 2)^2 (r - 1)^4 (r + 1)^5 (r + 2)^2 (r + 3)) + (5 (r^3 + r^2 - 17 r + 55) Cos[(r + 6) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3) (r + 4)) - Cos[(r + 10) z]/((r + 1) (r + 2) (r + 3) (r + 4) (r + 5))) q^5 + (1/2949120) (Cos[(r - 12) z]/((r - 6) (r - 5) (r - 4) (r - 3) (r - 2) (r - 1)) - (6 (r^3 - r^2 - 31 r - 89) Cos[(r - 8) z])/ ((r - 5) (r - 4) (r - 3) (r - 2) (r - 1)^3 (r + 1)^2) + (15 (r^10 - 3 r^9 - 53 r^8 + 69 r^7 + 145 r^6 + 8211 r^5 - 16879 r^4 - 32025 r^3 + 32954 r^2 + 16404 r + 71528) Cos[(r - 4) z])/ ((r - 4) (r - 3) (r - 2)^3 (r - 1)^5 (r + 1)^4 (r + 2)^2) - (20 (r^14 - 72 r^12 + 597 r^10 + 75244 r^8 - 718317 r^6 + 153312 r^4 + 4883287 r^2 + 1329084) Cos[r z])/((r - 3)^2 (r - 2)^2 (r - 1)^6 (r + 1)^6 (r + 2)^2 (r + 3)^2) + (15 (r^10 + 3 r^9 - 53 r^8 - 69 r^7 + 145 r^6 - 8211 r^5 - 16879 r^4 + 32025 r^3 + 32954 r^2 - 16404 r + 71528) Cos[(r + 4) z])/ ((r - 2)^2 (r - 1)^4 (r + 1)^5 (r + 2)^3 (r + 3) (r + 4)) - (6 (r^3 + r^2 - 31 r + 89) Cos[(r + 8) z])/((r - 1)^2 (r + 1)^3 (r + 2) (r + 3) (r + 4) (r + 5)) + Cos[(r + 12) z]/((r + 1) (r + 2) (r + 3) (r + 4) (r + 5) (r + 6))) q^6 + O[q]^7 /; !(Element[r, Integers] && -6 <= r <= 6)










Standard Form





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</mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 122880 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 55 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 9 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 273 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2457 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1931 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6335 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3572 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 7564 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 9 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 273 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2457 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1931 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6335 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3572 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 7564 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 17 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 55 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2949120 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> - </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 89 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 10 </mn> </msup> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 53 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 69 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 145 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8211 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16879 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 32025 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32954 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16404 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 71528 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 14 </mn> </msup> <mo> - </mo> <mrow> <mn> 72 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 597 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 75244 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 718317 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 153312 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4883287 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1329084 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> r </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 10 </mn> </msup> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 53 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 69 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 145 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8211 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16879 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32025 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32954 </mn> <mo> &#8290; </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16404 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 71528 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> + </mo> <msup> <mi> r </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <mn> 89 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> r </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 7 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> r </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> &#8804; </mo> <mi> r </mi> <mo> &#8804; </mo> <mn> 6 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Ce </ci> <apply> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> r </ci> </apply> <ci> q </ci> </apply> <ci> q </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <cos /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> q </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 32 </cn> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 384 </cn> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <cn type='integer'> -11 </cn> </apply> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <cn type='integer'> 11 </cn> </apply> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6144 </cn> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -8 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> -29 </cn> </apply> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 185 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 675 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 316 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7 </cn> <ci> r </ci> </apply> </apply> <cn type='integer'> 29 </cn> </apply> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 8 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 122880 </cn> <apply> <plus /> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -10 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> 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<cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <cos /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 12 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 5 </cn> </apply> <apply> <plus /> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> q </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> r </ci> <integers /> </apply> <apply> <leq /> <cn type='integer'> -6 </cn> <ci> r </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998-2014 Wolfram Research, Inc.