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1: Bibliography I
  • K. Inkeri (1959) The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
  • 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.
  • M. E. H. Ismail and D. R. Masson (1991) Two families of orthogonal polynomials related to Jacobi polynomials. Rocky Mountain J. Math. 21 (1), pp. 359–375.
  • M. E. H. Ismail (2000a) An electrostatics model for zeros of general orthogonal polynomials. Pacific J. Math. 193 (2), pp. 355–369.
  • M. E. H. Ismail (2005) Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
  • 2: Bibliography B
  • E. Bannai (1990) Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics. In Orthogonal Polynomials (Columbus, OH, 1989), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.
  • P. Baratella and L. Gatteschi (1988) The Bounds for the Error Term of an Asymptotic Approximation of Jacobi Polynomials. In Orthogonal Polynomials and Their Applications (Segovia, 1986), Lecture Notes in Math., Vol. 1329, pp. 203–221.
  • P. Bleher and A. Its (1999) Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1), pp. 185–266.
  • R. Bo and R. Wong (1999) A uniform asymptotic formula for orthogonal polynomials associated with exp ( x 4 ) . J. Approx. Theory 98, pp. 146–166.
  • C. Brezinski (1980) Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
  • 3: 18.5 Explicit Representations
    §18.5 Explicit Representations
    §18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
    Hermite
    4: Bibliography P
  • A. M. Parkhurst and A. T. James (1974) Zonal Polynomials of Order 1 Through 12 . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.
  • P. I. Pastro (1985) Orthogonal polynomials and some q -beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (2), pp. 517–540.
  • J. Patera and P. Winternitz (1973) A new basis for the representation of the rotation group. Lamé and Heun polynomials. J. Mathematical Phys. 14 (8), pp. 1130–1139.
  • M. D. Perlman and I. Olkin (1980) Unbiasedness of invariant tests for MANOVA and other multivariate problems. Ann. Statist. 8 (6), pp. 1326–1341.
  • R. Piessens (1982) Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.
  • 5: Bibliography W
  • J. Walker (1988) Shadows cast on the bottom of a pool are not like other shadows. Why?. Scientific American 259, pp. 86–89.
  • X.-S. Wang and R. Wong (2012) Asymptotics of orthogonal polynomials via recurrence relations. Anal. Appl. (Singap.) 10 (2), pp. 215–235.
  • R. S. Ward (1987) The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.
  • J. A. Wilson (1978) Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials. Ph.D. Thesis, University of Wisconsin, Madison, WI.
  • J. A. Wilson (1980) Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11 (4), pp. 690–701.
  • 6: Bibliography S
  • H. E. Salzer (1955) Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms. Math. Tables Aids Comput. 9 (52), pp. 164–177.
  • B. Simon (2005a) Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
  • B. Simon (2005b) Orthogonal Polynomials on the Unit Circle. Part 2: Spectral Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
  • J. R. Stembridge (1995) A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.
  • G. Szegő (1967) Orthogonal Polynomials. 3rd edition, American Mathematical Society, New York.
  • 7: 3.8 Nonlinear Equations
    §3.8(iii) Other Methods
    For the computation of zeros of orthogonal polynomials as eigenvalues of finite tridiagonal matrices (§3.5(vi)), see Gil et al. (2007a, pp. 205–207). … The polynomialConsider x = 20 and j = 19 . We have p ( 20 ) = 19 ! and a 19 = 1 + 2 + + 20 = 210 . …
    8: Bibliography
  • A. Adelberg (1992) On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.
  • W. A. Al-Salam and L. Carlitz (1965) Some orthogonal q -polynomials. Math. Nachr. 30, pp. 47–61.
  • R. Askey and M. E. H. Ismail (1984) Recurrence relations, continued fractions, and orthogonal polynomials. Mem. Amer. Math. Soc. 49 (300), pp. iv+108.
  • R. Askey and J. Wilson (1985) Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc. 54 (319), pp. iv+55.
  • R. Askey (1975b) Orthogonal Polynomials and Special Functions. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 21, Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • 9: 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.
  • 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 (1975c) Two-variable Analogues of the Classical Orthogonal Polynomials. In Theory and Application of Special Functions, R. A. Askey (Ed.), pp. 435–495.
  • 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.
  • T. Kriecherbauer and K. T.-R. McLaughlin (1999) Strong asymptotics of polynomials orthogonal with respect to Freud weights. Internat. Math. Res. Notices 1999 (6), pp. 299–333.