A372268 Decimal expansion of the largest positive zero of the Legendre polynomial of degree 4.
8, 6, 1, 1, 3, 6, 3, 1, 1, 5, 9, 4, 0, 5, 2, 5, 7, 5, 2, 2, 3, 9, 4, 6, 4, 8, 8, 8, 9, 2, 8, 0, 9, 5, 0, 5, 0, 9, 5, 7, 2, 5, 3, 7, 9, 6, 2, 9, 7, 1, 7, 6, 3, 7, 6, 1, 5, 7, 2, 1, 9, 2, 0, 9, 0, 6, 5, 2, 9, 4, 7, 1, 4, 9, 5, 0, 4, 8, 8, 6, 5, 7, 0, 4, 1, 6, 2
Offset: 0
Examples
0.861136311594052575223946488892809505095725379629717637615721...
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=4
- Wikipedia, Legendre polynomials.
- Index entries for algebraic numbers, degree 4.
Crossrefs
Programs
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Mathematica
First[RealDigits[Root[LegendreP[4, #] &, 4], 10, 100]] (* Paolo Xausa, Feb 27 2025 *)
Formula
Largest positive root of 35*x^4 - 30*x^2 + 3 = 0.
Equals sqrt((3+2*sqrt(6/5))/7).