A372274 - OEIS

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

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OFFSET

0,1

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..10000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Table 25.4, n=7.

A.H.M. Smeets, Python program for Legendre-Gauss quadrature constants.

Eric Weisstein's World of Mathematics, Legendre Polynomial.

Eric Weisstein's World of Mathematics, Legendre-Gauss Quadrature.

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...

MATHEMATICA

First[RealDigits[Root[LegendreP[7, #] &, 5], 10, 100]] (* Paolo Xausa, Feb 27 2025 *)

PROG