Theory and Modern Applications
n | \(L_{n}(\eta )\) |
---|---|
0 | 1 |
1 | η |
2 | \(\frac{1}{2} (3 \eta ^{2}-1 )\) |
3 | \(\frac{1}{2} (5 \eta ^{3}-3 \eta )\) |
4 | \(\frac{1}{8} (35 \eta ^{4}-30 \eta ^{2}+3 )\) |
5 | \(\frac{1}{8} (63 \eta ^{5}-70 \eta ^{3}+15 \eta )\) |
6 | \(\frac{1}{16} (231 \eta ^{6}-315 \eta ^{4}+105 \eta ^{2}-5 )\) |
7 | \(\frac{1}{16} (429 \eta ^{7}-693 \eta ^{5}+315 \eta ^{3}-35 \eta )\) |
8 | \(\frac{1}{128} (6435 \eta ^{8}-12{,}012 \eta ^{6}+6930 \eta ^{4}-1260 \eta ^{2}+35 )\) |
9 | \(\frac{1}{128} (12{,}155 \eta ^{9}-25{,}740 \eta ^{7}+18{,}018 \eta ^{5}-4620 \eta ^{3}+315 \eta )\) |
10 | \(\frac{1}{256} (46{,}189 \eta ^{10}-109{,}395 \eta ^{8}+90{,}090 \eta ^{6}-30{,}030 \eta ^{4}+3465 \eta ^{2}-63 )\) |