A372268 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 4.

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Wikipedia, Legendre polynomials.

Index entries for algebraic numbers, degree 4.

Formula

Largest positive root of 35*x^4 - 30*x^2 + 3 = 0.

Equals sqrt((3+2*sqrt(6/5))/7).

Example

0.861136311594052575223946488892809505095725379629717637615721...

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: A329090 A197759 A199070 * A011009 A155184 A153101

Adjacent sequences: A372265 A372266 A372267 * A372269 A372270 A372271

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved