A372275 Decimal expansion of the middle positive zero of the Legendre polynomial of degree 7.

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

Offset

0,1

Links

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

Wikipedia, Legendre polynomials.

Index entries for algebraic numbers, degree 6.

Formula

Middle positive root of 429*x^6 - 693*x^4 + 315*x^2 - 35 = 0.

Example

0.741531185599394439863864773280788407074147647141390260119955...

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: A371851 A199157 A328416 * A010508 A070403 A144468

Adjacent sequences: A372272 A372273 A372274 * A372276 A372277 A372278

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved