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Asymptotics for the zeros of the generalized Bessel polynomials. (English) Zbl 0782.33003
See the preview in Zbl 0735.33001.

33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
30C15Zeros of polynomials, etc. (one complex variable)
Full Text: DOI EuDML
[1] Buckholtz, J.D. (1966): A characterization of the exponential series. Amer. Math. Monthly73, Part II, 121-123 · Zbl 0146.09801 · doi:10.2307/2313761
[2] Carpenter, A.J. (1988): Some theoretical and computational aspects of approximation theory. Ph.D. Thesis, Univ. of Leeds, Leeds, England
[3] Carpenter, A.J., Varga, R.S., Waldvogel, J. (1991): Asymptotics for the zeros of the partial sums of ez. I. Rocky Mount. J. Math.21, 99-120 · Zbl 0734.30008 · doi:10.1216/rmjm/1181072998
[4] de Bruin, M.G., Saff, E.B., Varga, R.S. (1981): On the zeros of generalized Bessel polynomials, I and II. Indag. Math.43, 1-25 · Zbl 0467.33004
[5] Grosswald, E. (1978): Bessel polynomials, Lecture notes in mathematics, vol. 698. Springer, Berlin Heidelberg New York · Zbl 0416.33008
[6] Olver, F.W.J. (1954): The asymptotic expansions of Bessel functions of large order. Phil. Trans. Roy. Soc. London Ser. A247, 338-368
[7] Saff, E.B., Varga, R.S. (1975): On the zeros and poles of Pad? approximants to ez. Numer. Math.25, 1-14 · Zbl 0322.41010 · doi:10.1007/BF01419524
[8] Saff, E.B., Varga, R.S. (1976): Zero-free parabolic regions for sequences of polynomials. SIAM J. Math. Anal.7, 344-357 · Zbl 0332.30001 · doi:10.1137/0507028
[9] Saff, E.B., Varga, R.S. (1976): On the sharpness of theorems concerning zero-free regions for certain sequences of polynomials. Numer. Math.26, 345-354 · Zbl 0339.26018 · doi:10.1007/BF01409957
[10] Saff, E.B., Varga, R.S. (1977): On the zeros and poles of Pad? approximants to ez. II. In: Pad? and Rational Approximations: Theory and Applications. Academic Press, New York, pp. 195-213
[11] Saff, E.B., Varga, R.S. (1978): On the zeros and poles of Pad? approximants to ez. III. Numer. Math.30, 241-266 · Zbl 0438.41015 · doi:10.1007/BF01411842
[12] Szeg?, G. (1924): ?ber eine Eigenschaft der Exponentialreihe. Sitzungsber. Berl. Math. Ges.23, 50-64 · Zbl 50.0257.01
[13] Varga, R.S. (1982): Topics in polynomial and rational interpolation and approximation, Collection s?minaire de math?matiques sup?rieures, vol. 81. Les Presses de l’Universit? de Montr?al, Montr?al