ZEROS AND STIELTJES CONTINUED FRACTION FOR

L. R. Shenton (U. S. A.) and K. O. Bowman (U. S. A.)

Received August 14, 2008

References:

[1] A. C. Aitken and H. T. Gonin, On fourfold sampling with and without replacement, Proc. Roy. Soc. Edinburgh LV (1934-1935), 114-125. [2] J. I’A. Bromwich, An Introduction to the Theory of Infinite Series, McMillan, London, 1926. [3] B. W. Char, On Stieltjes’ continued fraction for the gamma function, Math. Comp. 34(150) (1980), 547-551. [4] R. W. D. Nickalls, A new approach to solving the cubic: Cardan’s solution revealed, Math. Gazette 77 (1993), 354-359. [5] T. J. Stieltjes, Correspondence d’Hermite et de Stieltjes, Gauthier-Villars, Paris, 1905. [6] T. J. Stieltjes, Oeuvres Complétes, Tome 2, P. Noordhoff, Groningen, 1918. [7] G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., XXIII, Amer. Math. Soc., New York, 1939. [8] H. S. Wall, Continued Fractions, Chelsea Publishing Co., Bronx, New York, 1948.

Keywords and phrases: largest zeros, Maple code, orthogonal system, probability models.