A372274 Decimal expansion of the smallest positive zero of the Legendre polynomial of degree 7.

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

Offset

0,1

Links

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

Wikipedia, Legendre polynomials.

Index entries for algebraic numbers, degree 6.

Formula

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

Example

0.405845151377397166906606412076961463347382014099370126387043...

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: A102293 A198747 A021965 * A355921 A164108 A064520

Adjacent sequences: A372271 A372272 A372273 * A372275 A372276 A372277

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved