Truncation error bounds for modified continued fractions with applications to special functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:

Affiliation:

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;x₁), 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:	KeywordHeading" >Subject Classifications AMS(MOS): 65D20 30B70 30E10 41A20 CR: G1.2
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