A372273 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 6.

9, 3, 2, 4, 6, 9, 5, 1, 4, 2, 0, 3, 1, 5, 2, 0, 2, 7, 8, 1, 2, 3, 0, 1, 5, 5, 4, 4, 9, 3, 9, 9, 4, 6, 0, 9, 1, 3, 4, 7, 6, 5, 7, 3, 7, 7, 1, 2, 2, 8, 9, 8, 2, 4, 8, 7, 2, 5, 4, 9, 6, 1, 6, 5, 2, 6, 6, 1, 3, 5, 0, 0, 8, 4, 4, 2, 0, 0, 1, 9, 6, 2, 7, 6, 2, 8, 8

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Wikipedia, Legendre polynomials.

Index entries for algebraic numbers, degree 6.

Formula

Largest positive root of 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.

Example

0.932469514203152027812301554493994609134765737712289824872549...

Mathematica

First[RealDigits[Root[LegendreP[6, #] &, 6], 10, 100]] (* Paolo Xausa, Feb 27 2025 *)

Prog

(PARI) polrootsreal(pollegendre(6))[6] \\ Charles R Greathouse IV, Nov 17 2025

Crossrefs

Cf. A008316, A100258.

There are floor(k/2) positive zeros of the Legendre polynomial of degree k:

k | zeros

---+--------------------------

2 | A020760

3 | A010513/10

4 | A372267, A372268

5 | A372269, A372270

6 | A372271, A372272, A372273

7 | A372274, A372275, A372276

Sequence in context: A195704 A176516 A337768 * A210644 A072559 A019941

Adjacent sequences: A372270 A372271 A372272 * A372274 A372275 A372276

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved