The On-Line Encyclopedia of Integer Sequences (OEIS)

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A372273

Decimal expansion of the largest positive zero of the Legendre polynomial of degree 6.
(history; published version)

#8 by Amiram Eldar at Tue Apr 30 02:26:47 EDT 2024

STATUS

reviewed

approved

#7 by Joerg Arndt at Tue Apr 30 02:10:46 EDT 2024

STATUS

proposed

reviewed

#6 by Pontus von Brömssen at Mon Apr 29 10:20:35 EDT 2024

STATUS

editing

proposed

#5 by Pontus von Brömssen at Mon Apr 29 10:16:33 EDT 2024

NAME

Decimal expansion of the largest positive root zero of the Legendre polynomial of degree 6.

STATUS

approved

editing

#4 by N. J. A. Sloane at Sun Apr 28 11:57:49 EDT 2024

STATUS

proposed

approved

#3 by Pontus von Brömssen at Thu Apr 25 16:08:33 EDT 2024

STATUS

editing

proposed

#2 by Pontus von Brömssen at Thu Apr 25 15:46:05 EDT 2024

NAME

allocated for Pontus von BrömssenDecimal expansion of the largest positive root of the Legendre polynomial of degree 6.

DATA

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

OFFSET

0,1

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre polynomials</a>.

<a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a>.

FORMULA

Largest positive root of 231*x^6 - 315*x^4 + 105*x^2 - 5 = 0.

EXAMPLE

0.932469514203152027812301554493994609134765737712289824872549...

CROSSREFS

Cf. A008316, A100258.

There are floor(k/2) positive zeros of the Legendre polynomial of degree k: