A372269 Decimal expansion of the smallest positive zero of the Legendre polynomial of degree 5.

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

Offset

0,1

Links

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

Wikipedia, Legendre polynomials.

Index entries for algebraic numbers, degree 4.

Formula

Smallest positive root of 63*x^4 - 70*x^2 + 15 = 0.

Equals sqrt(5-2*sqrt(10/7))/3.

Example

0.538469310105683091036314420700208804967286606905559956202231...

Mathematica

First[RealDigits[Root[LegendreP[5, #] &, 4], 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: A093203 A021654 A021069 * A237192 A161488 A010484

Adjacent sequences: A372266 A372267 A372268 * A372270 A372271 A372272

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved