A372276 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 7.

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

Offset

0,1

Links

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

Wikipedia, Legendre polynomials.

Index entries for algebraic numbers, degree 6.

Formula

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

Example

0.949107912342758524526189684047851262400770937670617783548769...

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: A103742 A092736 A019617 * A200296 A021517 A154977

Adjacent sequences: A372273 A372274 A372275 * A372277 A372278 A372279

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved