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Home All issues Volume 691 (November 2024) A&A, 691 (2024) L3 Full HTML
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Table A.1.

Eccentricity polynomials, Glpq(e), from Cayley (1861), up to order 7 in eccentricity.

l p q Glpq(e)
2 0 -7 15625 129024 e 7 $ \frac{15625}{129024}e^7 $
2 0 -6 4 45 e 6 $ \frac{4}{45}e^6 $
2 0 -5 81 1280 e 5 + 81 2048 e 7 $ \frac{81}{1280}e^5 +\frac{81}{2048}e^7 $
2 0 -4 1 24 e 4 + 7 240 e 6 $ \frac{1}{24}e^4 +\frac{7}{240}e^6 $
2 0 -3 1 48 e 3 + 11 768 e 5 + 313 30720 e 7 $ \frac{1}{48}e^3 +\frac{11}{768}e^5 +\frac{313}{30720}e^7 $
2 0 -2 0
2 0 -1 − 1 2 e + 1 16 e 3 − 5 384 e 5 − 143 18432 e 7 $ -\frac{1}{2}e +\frac{1}{16}e^3 -\frac{5}{384}e^5 -\frac{143}{18432}e^7 $
2 0 0 1 − 5 2 e 2 + 13 16 e 4 − 35 288 e 6 $ 1 -\frac{5}{2}e^2 +\frac{13}{16}e^4 -\frac{35}{288}e^6 $
2 0 1 7 2 e − 123 16 e 3 + 489 128 e 5 − 1763 2048 e 7 $ \frac{7}{2}e -\frac{123}{16}e^3 +\frac{489}{128}e^5 -\frac{1763}{2048}e^7 $
2 0 2 17 2 e 2 − 115 16 e 4 + 601 48 e 6 $ \frac{17}{2}e^2 -\frac{115}{16}e^4 +\frac{601}{48}e^6 $
2 0 3 845 48 e 3 − 32525 768 e 5 + 208225 6144 e 7 $ \frac{845}{48} e^3 -\frac{32525}{768} e^5 +\frac{208225}{6144} e^7 $
2 0 4 533 16 e 4 − 13827 160 e 6 $ \frac{533}{16} e^4 -\frac{13827}{160} e^6 $
2 0 5 228347 3840 e 5 − 3071075 18432 e 7 $ \frac{228347}{3840} e^5 -\frac{3071075}{18432} e^7 $
2 0 6 73369 720 e 6 $ \frac{73369}{720} e^6 $
2 0 7 12144273 71680 e 7 $ \frac{12144273}{71680} e^7 $
2 1 -7 G217(e)
2 1 -6 G216(e)
2 1 -5 G215(e)
2 1 -4 G214(e)
2 1 -3 G213(e)
2 1 -2 G212(e)
2 1 -1 G211(e)
2 1 0 ( 1 − e 2 ) − 3 / 2 ≃ 1 + 3 2 e 2 + 15 8 e 4 + 35 16 e 6 + O ( e 9 ) $ (1 -e^2)^{-3/2} \simeq 1 +\frac{3}{2}e^2 +\frac{15}{8}e^4 +\frac{35}{16}e^6 +\mathcal{O}(e^9) $
2 1 1 3 2 e + 27 16 e 3 + 261 128 e 5 + 14309 6144 e 7 $ \frac{3}{2}e +\frac{27}{16}e^3 +\frac{261}{128}e^5 +\frac{14309}{6144}e^7 $
2 1 2 9 4 e 2 + 7 4 e 4 + 141 64 e 6 $ \frac{9}{4}e^2 +\frac{7}{4}e^4 +\frac{141}{64}e^6 $
2 1 3 53 16 e 3 + 393 256 e 5 + 24753 10240 e 7 $ \frac{53}{16}e^3 +\frac{393}{256}e^5 +\frac{24753}{10240}e^7 $
2 1 4 77 16 e 4 + 129 160 e 6 $ \frac{77}{16}e^4 +\frac{129}{160}e^6 $
2 1 5 1773 256 e 5 − 4987 6144 e 7 $ \frac{1773}{256}e^5 -\frac{4987}{6144}e^7 $
2 1 6 3167 320 e 6 $ \frac{3167}{320}e^6 $
2 1 7 432091 30720 e 7 $ \frac{432091}{30720}e^7 $

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