Abstract
The purpose of this paper is to show the symmetric relations that appear between the coefficients of some even and odd extensions of the M-fractions related to a certain kind of symmetric strong Stieltjes distribution.
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Bracciali, C. F.: Relations between certain symmetric strong Stieltjes distributions, In: B. Berndt and F. Gesztesy (eds), Continued Fractions: from Analytic Number Theory to Constructive Approximation, Contemp. Math. Ser. 236, Amer. Math. Soc., Providence, 1999, pp. 71–83.
Bracciali, C. F., McCabe, J. H. and Sri Ranga, A.: On a symmetry in strong distributions,J. Comput. Appl. Math. 105 (1999), 187–198.
Common, A. K. and McCabe, J. H.: Continued fractions for symmetric strong Stieltjes moment problems, In: A. Cuyt (ed.), Nonlinear Numerical Methods and Rational Approximation II, Math. Appl. 296, Kluwer Acad. Publ., Dordrecht, 1994, pp. 387–394.
Common, A. K. and McCabe, J. H.: The symmetric strong moment problem, J. Comput. Appl. Math. 67 (1996), 327–341.
Henrici, P.: Applied and Computational Complex Analysis, Vol. 1, Wiley, New York, 1974.
Jones, W. B., Magnus, A. and Thron, W. J.: PC-fractions and orthogonal Laurent polynomials for log-normal distributions, J. Math. Anal. Appl. 170(1992), 225–244.
Jones, W. B., Njåstad, O. and Thron, W. J.: Two-point Padé expansions for a family of analytic functions, J. Comput. Appl. Math. 9 (1983), 105–123.
Jones, W. B., Njåstad, O. and Thron, W. J.: Continued fractions associated with trigonometric and other strong moment problems, Constr. Approx. 2 (1986), 197–211.
Jones, W. B., Njåstad, O. and Thron, W. J.:Moment theory, orthogonal polynomials, quadrature and continued fractions associated with the unit circle, Bull. London Math. Soc. 21 (1989), 113–152.
Jones, W. B. and Thron, W. J.: ContinuedFractions: Analytic Theory and Applications, Encyclop. Math. Appl. 11, Addison-Wesley, Reading, Mass, 1980.
Jones, W. B., Thron, W. J. and Waadeland, H.: A strong Stieltjes moment problem, Trans. Amer. Math. Soc. 261 (1980), 503–528.
Lorentzen, L. and Waadeland, H.: Continued Fractions with Applications, Stud. Comput.Math. 3, North-Holland, Amsterdam, 1992.
McCabe, J. H.: A formal extension of the Padé table to include two-point Padé quotients, J. Inst. Math. Appl. 15 (1975), 363–372.
McCabe, J. H.: On the even extension of an M-fraction, In: M. de Bruin and H. van Rossum (eds), Padé Approximation and its Applications, Lecture Notes in Math. 888, Springer-Verlag, New York, 1981, pp. 290–299.
Sri Ranga, A.: Another quadrature rule of highest algebraic degree of precision, Numer. Math. 68 (1994), 283–294.
Sri Ranga, A., de Andrade, E. X. L. and McCabe, J. H.: Some consequences of a symmetry in strong distributions, J. Math. Anal. Appl. 193 (1995), 158–168.
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Bracciali, C.F., McCabe, J.H. Some Extensions of M-Fractions Related to Strong Stieltjes Distributions. Acta Applicandae Mathematicae 61, 65–80 (2000). https://doi.org/10.1023/A:1006428017077
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DOI: https://doi.org/10.1023/A:1006428017077