Where each entry of Legendre polynomials came from

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51 entries.

n value last changed by
0 1 2026-08-09flattening
1 x 2026-08-09flattening
2 3/2*x^2 - 1/2 2026-08-09flattening
3 5/2*x^3 - 3/2*x 2026-08-09flattening
4 35/8*x^4 - 15/4*x^2 + 3/8 2026-08-09flattening
5 63/8*x^5 - 35/4*x^3 + 15/8*x 2026-08-09flattening
6 231/16*x^6 - 315/16*x^4 + 105/16*x^2 - 5/16 2026-08-09flattening
7 429/16*x^7 - 693/16*x^5 + 315/16*x^3 - 35/16*x 2026-08-09flattening
8 6435/128*x^8 - 3003/32*x^6 + 3465/64*x^4 - 315/32*x^2 + 35/128 2026-08-09flattening
9 12155/128*x^9 - 6435/32*x^7 + 9009/64*x^5 - 1155/32*x^3 + 315/128*x 2026-08-09flattening
10 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 346… 2026-08-09flattening
11 88179/256*x^11 - 230945/256*x^9 + 109395/128*x^7 - 45045/128*x^5 + 15… 2026-08-09flattening
12 676039/1024*x^12 - 969969/512*x^10 + 2078505/1024*x^8 - 255255/256*x^… 2026-08-09flattening
13 1300075/1024*x^13 - 2028117/512*x^11 + 4849845/1024*x^9 - 692835/256*… 2026-08-09flattening
14 5014575/2048*x^14 - 16900975/2048*x^12 + 22309287/2048*x^10 - 1454953… 2026-08-09flattening
15 9694845/2048*x^15 - 35102025/2048*x^13 + 50702925/2048*x^11 - 3718214… 2026-08-09flattening
16 300540195/32768*x^16 - 145422675/4096*x^14 + 456326325/8192*x^12 - 18… 2026-08-09flattening
17 583401555/32768*x^17 - 300540195/4096*x^15 + 1017958725/8192*x^13 - 4… 2026-08-09flattening
18 2268783825/65536*x^18 - 9917826435/65536*x^16 + 4508102925/16384*x^14… 2026-08-09flattening
19 4418157975/65536*x^19 - 20419054425/65536*x^17 + 9917826435/16384*x^1… 2026-08-09flattening
20 34461632205/262144*x^20 - 83945001525/131072*x^18 + 347123925225/2621… 2026-08-09flattening
21 67282234305/262144*x^21 - 172308161025/131072*x^19 + 755505013725/262… 2026-08-09flattening
22 263012370465/524288*x^22 - 1412926920405/524288*x^20 + 3273855059475/… 2026-08-09flattening
23 514589420475/524288*x^23 - 2893136075115/524288*x^21 + 7064634602025/… 2026-08-09flattening
24 8061900920775/4194304*x^24 - 11835556670925/1048576*x^22 + 6075585757… 2026-08-09flattening
25 15801325804719/4194304*x^25 - 24185702762325/1048576*x^23 + 130191123… 2026-08-09flattening
26 61989816618513/8388608*x^26 - 395033145117975/8388608*x^24 + 55627116… 2026-08-09flattening
27 121683714103007/8388608*x^27 - 805867616040669/8388608*x^25 + 1185099… 2026-08-09flattening
28 956086325095055/33554432*x^28 - 3285460280781189/16777216*x^26 + 2014… 2026-08-09flattening
29 1879204156221315/33554432*x^29 - 6692604275665385/16777216*x^27 + 427… 2026-08-09flattening
30 7391536347803839/67108864*x^30 - 54496920530418135/67108864*x^28 + 18… 2026-08-09flattening
31 14544636039226909/67108864*x^31 - 110873045217057585/67108864*x^29 + … 2026-08-09flattening
32 916312070471295267/2147483648*x^32 - 450883717216034179/134217728*x^3… 2026-08-09flattening
33 1804857108504066435/2147483648*x^33 - 916312070471295267/134217728*x^… 2026-08-09flattening
34 7113260368810144185/4294967296*x^34 - 59560284580634192355/4294967296… 2026-08-09flattening
35 14023284727082855679/4294967296*x^35 - 120925426269772451145/42949672… 2026-08-09flattening
36 110628135069209194801/17179869184*x^36 - 490814965447899948765/858993… 2026-08-09flattening
37 218266320541953276229/17179869184*x^37 - 995653215622882753209/858993… 2026-08-09flattening
38 861577581086657669325/34359738368*x^38 - 8075853860052271220473/34359… 2026-08-09flattening
39 1701063429324939500975/34359738368*x^39 - 16369974040646495717175/343… 2026-08-09flattening
40 26876802183334044115405/274877906944*x^40 - 66341473743672640538025/6… 2026-08-09flattening
41 53098072606098965203605/274877906944*x^41 - 134384010916670220577025/… 2026-08-09flattening
42 209863810776486386280915/549755813888*x^42 - 217702097685005757334780… 2026-08-09flattening
43 414847067813984717066925/549755813888*x^43 - 440714002630621411189921… 2026-08-09flattening
44 3281063172710606398620225/2199023255552*x^44 - 1783842391600134283387… 2026-08-09flattening
45 6489213830472088210604445/2199023255552*x^45 - 3609169489981667038482… 2026-08-09flattening
46 25674715590128696833261065/4398046511104*x^46 - 292014622371243969477… 2026-08-09flattening
47 50803160635786570329644235/4398046511104*x^47 - 590518458572960027165… 2026-08-09flattening
48 1608766753466574727105400775/70368744177664*x^48 - 238774854988196880… 2026-08-09flattening
49 3184701532372607112841303575/70368744177664*x^49 - 482630026039972418… 2026-08-09flattening
50 12611418068195524166851562157/140737488355328*x^50 - 1560503750862577… 2026-08-09flattening