A regular continued C-fraction is associated with a power series. The coefficients of this fraction are determined via either Hankel determinants or inverse derivatives. We prove the equivalence of these approaches to the construction of regular continued C-fractions.
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References
H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York (1948).
O. Perron, Die Lehre von den Kettenbruchen, Vol. 2, Teubner, Stuttgart (1957).
W. B. Jones and W. J. Tron, Continued Fractions: Analytic Theory and Applications, Addison-Wesley, Reading (1980).
V. Ya. Skorobogat'ko, Theory of Branching Fractions and Its Application in Computational Mathematics [in Russian], Nauka, Moscow (1983).
T. N. Thiele, Interpolationsprechnung, Teubner, Leipzig (1909).
M. M. Pahirya and R. A. Katsala, “Expansions of some functions in continued fractions,” Nauk. Visn. Uzhhorod Univ., Ser. Mat. Inform., Issue 14–15, 107–116 (2007).
N. E. Norlund, Vorlesungen uber Differenzenrechnung, Springer, Berlin (1924).
R. A. Katsala, “Relationship between inverse derivatives and derivatives of functions of one real variable,” Nauk. Visn. Uzhhorod Univ., Ser. Mat. Inform., Issue 16, 73–81 (2008).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 1005–1008, July, 2009.
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Pahirya, M.M., Katsala, R.A. Equivalence of two methods for construction of regular continued C-fractions. Ukr Math J 61, 1192–1198 (2009). https://doi.org/10.1007/s11253-009-0268-z
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DOI: https://doi.org/10.1007/s11253-009-0268-z