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Truncation error bounds for modified continued fractions with applications to special functions

Authors:

Institution:

1. Department of Mathematics, SUNY College at Oswego, 13126, Oswego, NY, USA
2. Department of Mathematics, University of Colorado, 80309-0426, Boulder, CO, USA

Abstract:

Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland 35] in 1980 that a limit-periodic MCFK(a _n, 1;x ₁), with $\mathop {\lim }\limits_{n \to \infty } a_n = :a \in \mathbb{C} - ( - \infty , - \tfrac{1}{4}]$ andnth approximant

$g_n = S_n (x_1 ) = \frac{{a_1 }}{1} + \frac{{a_2 }}{1} + \cdots + \frac{{a_{n - 1} }}{1} + \frac{{a_n }}{{1 + x_1 }},$

Keywords:	Subject Classifications" target="_blank">Subject Classifications AMS(MOS): 65D20 30B70 30E10 41A20 CR: G1 2
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