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Sobolev orthogonal polynomials


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1: 18.36 Miscellaneous Polynomials
§18.36(ii) Sobolev Orthogonal Polynomials
2: Bibliography M
  • F. Marcellán, M. Alfaro, and M. L. Rezola (1993) Orthogonal polynomials on Sobolev spaces: Old and new directions. J. Comput. Appl. Math. 48 (1-2), pp. 113–131.
  • F. Marcellán and Y. Xu (2015) On Sobolev orthogonal polynomials. Expo. Math. 33 (3), pp. 308–352.
  • 3: Bibliography G
  • W. Gautschi (2004) Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation, Oxford University Press, New York.
  • 4: Bibliography I
  • A. Iserles, P. E. Koch, S. P. Nørsett, and J. M. Sanz-Serna (1991) On polynomials orthogonal with respect to certain Sobolev inner products. J. Approx. Theory 65 (2), pp. 151–175.
  • 5: Bibliography E
  • W. N. Everitt, L. L. Littlejohn, and R. Wellman (2004) The Sobolev orthogonality and spectral analysis of the Laguerre polynomials { L n k } for positive integers k . J. Comput. Appl. Math. 171 (1-2), pp. 199–234.
  • 6: Bibliography K
  • E. G. Kalnins and W. Miller (1993) Orthogonal Polynomials on n -spheres: Gegenbauer, Jacobi and Heun. In Topics in Polynomials of One and Several Variables and their Applications, pp. 299–322.
  • S. F. Khwaja and A. B. Olde Daalhuis (2012) Uniform asymptotic approximations for the Meixner-Sobolev polynomials. Anal. Appl. (Singap.) 10 (3), pp. 345–361.
  • J. Koekoek, R. Koekoek, and H. Bavinck (1998) On differential equations for Sobolev-type Laguerre polynomials. Trans. Amer. Math. Soc. 350 (1), pp. 347–393.
  • W. Koepf (1999) Orthogonal polynomials and computer algebra. In Recent developments in complex analysis and computer algebra (Newark, DE, 1997), R. P. Gilbert, J. Kajiwara, and Y. S. Xu (Eds.), Int. Soc. Anal. Appl. Comput., Vol. 4, Dordrecht, pp. 205–234.
  • T. H. Koornwinder (2006) Lowering and Raising Operators for Some Special Orthogonal Polynomials. In Jack, Hall-Littlewood and Macdonald Polynomials, Contemp. Math., Vol. 417, pp. 227–238.