Application of solutions to the Thiele–Hermite problem for expanding the functions tg $z$, ctg $z$, th $z$, and cth $z$, in continued fractions
DOI:
https://doi.org/10.3842/umzh.v78i9-10.9920Keywords:
continued fractions, expanding functions into continued fractionsAbstract
UDC 517.518:519.652
A function of one complex variable can be expanded into a continued fraction by using one of the well-known methods based either on the Riccati differential equation, or on the Gauss hypergeometric series, or on the Hankel determinants, or on the reciprocal Thiele derivatives. The possibility of application of the solutions to the Thiele–Hermite problem with an aim of finding the coefficients of expansions of the functions tg $z$, ctg $z$, th $z$, and cth $z$ into continued fractions is analyzed.
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