A129337 Maximal possible degree of a Chebyshev-type quadrature formula with n nodes, in the case of the constant weight function on [ -1,1].

1, 3, 3, 5, 5, 7, 7, 7, 9, 9, 9, 9, 11, 11, 11, 11, 13, 13, 13, 13, 13, 15, 15, 15, 15

Offset

1,2

Comments

These are the results reported in reference [1]. Spherical designs in 3 dimensions (cf. A007828) also project to Chebyshev-type quadrature rules for the constant weight function on [ -1,1] (see reference [2]), but apparently this yields a smaller maximum degree for any given n.

Links

Table of n, a(n) for n=1..25.

Klaus-Jurgen Forster, Georg-Peter Ostermeyer, On Weighted Chebyshev-Type Quadrature Formulas,Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. 591-599. Table 1, p. 596.

Greg Kuperberg, Numerical Cubature from Archimedes' Hat-box Theorem, SIAM J. Numer. Anal. 44 (2006), no. 3, 908--935.

Crossrefs

Cf. A007828.

Sequence in context: A293702 A061794 A088524 * A133909 A177691 A206913

Adjacent sequences: A129334 A129335 A129336 * A129338 A129339 A129340

Keyword

more,nonn

Author

Paul Leopardi, May 28 2007

Status

approved