Abstract
For an integral power series with kernels symmetric in their arguments we find a corresponding integral continued fraction. We transform the series of Liouville and Laurent-Neumann, which are formal solutions of Fredholm integral equations of second kind, into corresponding RITZ and J-fractions. Using the J-fraction for the Laurent-Neumann series, we pass to the limit and thereby find a normal solution of equations of first kind. We give the asymptotics of the solution of linear differential equations in the form of a corresponding continued fraction.
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Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 96–109.
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Syavavko, M.S. Transformation of integral power series into corresponding continued fractions. J Math Sci 90, 2404–2415 (1998). https://doi.org/10.1007/BF02433975
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DOI: https://doi.org/10.1007/BF02433975