A372270 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 5.

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

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

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

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

Example

0.906179845938663992797626878299392965125651910762530862873762...

Mathematica

First[RealDigits[Root[LegendreP[5, #] &, 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: A173201 A345158 A019740 * A188738 A199789 A019874

Adjacent sequences: A372267 A372268 A372269 * A372271 A372272 A372273

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved