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associated Hermite polynomials

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11: Bibliography G
  • G. Gasper (1972) An inequality of Turán type for Jacobi polynomials. Proc. Amer. Math. Soc. 32, pp. 435–439.
  • W. Gautschi (2016) Algorithm 957: evaluation of the repeated integral of the coerror function by half-range Gauss-Hermite quadrature. ACM Trans. Math. Softw. 42 (1), pp. 9:1–9:10.
  • V. X. Genest, L. Vinet, and A. Zhedanov (2016) The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Proc. Amer. Math. Soc. 144 (12), pp. 5217–5226.
  • J. W. L. Glaisher (1940) Number-Divisor Tables. British Association Mathematical Tables, Vol. VIII, Cambridge University Press, Cambridge, England.
  • D. Gómez-Ullate and R. Milson (2014) Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials. J. Phys. A 47 (1), pp. 015203, 26 pp..
  • 12: Bibliography L
  • C. G. Lambe and D. R. Ward (1934) Some differential equations and associated integral equations. Quart. J. Math. (Oxford) 5, pp. 81–97.
  • D. A. Leonard (1982) Orthogonal polynomials, duality and association schemes. SIAM J. Math. Anal. 13 (4), pp. 656–663.
  • J. Letessier (1995) Co-recursive associated Jacobi polynomials. J. Comput. Appl. Math. 57 (1-2), pp. 203–213.
  • J. L. López and N. M. Temme (1999a) Approximation of orthogonal polynomials in terms of Hermite polynomials. Methods Appl. Anal. 6 (2), pp. 131–146.
  • J. L. López and N. M. Temme (1999b) Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials. J. Math. Anal. Appl. 239 (2), pp. 457–477.
  • 13: 18.2 General Orthogonal Polynomials
    §18.2(vi) Zeros
    §18.2(x) Orthogonal Polynomials and Continued Fractions
    Define the first associated monic orthogonal polynomials p n ( 1 ) ( x ) as monic OP’s satisfying … In fact, these are the only OP’s which are Sheffer polynomials (with Krawtchouk polynomials being only a finite system) …