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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.
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