A372271 Decimal expansion of the smallest positive zero of the Legendre polynomial of degree 6.

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

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 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.

Example

0.238619186083196908630501721680711935418610630140021350181395...

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: A073875 A356883 A377379 * A220395 A160099 A309967

Adjacent sequences: A372268 A372269 A372270 * A372272 A372273 A372274

Keyword

nonn,cons

Author

Pontus von Brömssen, Apr 25 2024

Status

approved