Abstract
Positive T-fractions are studied for analytic functions of the form
It is shown that such functions can be expressed as Stieltjes transforms and that the related moments can be computed by means of recurrence relations. The positive T-fraction coefficients are then computed using quotient-difference relations and the moments. Special attention is given to the approximation and computation in the complex plane of the two functions
by approximants f m (w) of the corresponding positive T-fraction. The rational functions f m (w) are two-point Padé approximants, and numerical experiments are given using various choices for the two points of interpolation. Contour maps of the number of significant digits S D(f m (w)) in the approximations f m (w) are used to describe the convergence behavior of the continued fraction at different parts of C and for different choices of interpolation points.
Keywords
- Significant Digit
- Branch Point
- Continue Fraction
- Interpolation Point
- Recurrence Formula
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Research supported in part by the U.S. National Science Foundation under Grant #DMS-8700498.
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© 1989 Springer-Verlag
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Jones, W.B., Wyshinski, N.J. (1989). Positive T-fraction expansions for a family of special functions. In: Jacobsen, L. (eds) Analytic Theory of Continued Fractions III. Lecture Notes in Mathematics, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096165
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DOI: https://doi.org/10.1007/BFb0096165
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