A372272 Decimal expansion of the middle positive zero of the Legendre polynomial of degree 6.

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

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

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

Example

0.661209386466264513661399595019905347006448564395170070814526...

Mathematica

First[RealDigits[Root[LegendreP[6, #] &, 5], 10, 100]] (* Paolo Xausa, Feb 27 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: A322622 A176565 A176567 * A283100 A065493 A133890

Adjacent sequences: A372269 A372270 A372271 * A372273 A372274 A372275

Keyword

nonn,cons,changed

Author

Pontus von Brömssen, Apr 25 2024

Status

approved