Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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Osculatory Thiele's interpolation continued fraction

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Mykhailo Pahirya
http://orcid.org/0000-0003-1488-3302
Yuliya Mislo
https://orcid.org/0000-0001-6771-2844

Abstract

A Thiele`s interpolation continued fraction with multiple knots is analogue to the Hermit interpolation polynomial in the theory of continued fractions. The problem of constructing an oscillatory (tangent) to the function f at the point z0 Thiele`s interpolation continued fraction (OICFT) is investigated in the paper. Only the values of the function f and its derivatives at the point z0 are used to calculate coefficients of OICFT. The proposed method of finding coefficients is based on the calculated values of sums of m-multiplicity and does not involve calculating the values of Hankel determinants.

Keywords:
Continued fraction, oscillatory interpolation, continuant

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How to Cite
Pahirya, M., & Mislo, Y. (2022). Osculatory Thiele’s interpolation continued fraction. Proceedings of the International Geometry Center, 15(2), 140-162. https://doi.org/10.15673/tmgc.v15i2.2296
Section
Papers
Author Biographies

Mykhailo Pahirya, Uzhhorod National University

Uzhhorod National University

Yuliya Mislo, Uzhhorod National University

Uzhhorod National University