We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known and new lacunary relations for the Bernoulli and Euler numbers.
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References
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, John Wiley and Sons, New York (1972).
NIST Handbook of Mathematical Functions, Cambridge Univ. Press, Cambridge (2010).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integral and Series. Vol. 3: More Special Functions, Gordon and Breach, New York (1990).
S. Ramanujan, “Some properties of Bernoulli’s numbers,” J. Ind. Math. Soc. No. 3, 219–234 (1911).
D. H. Lehmer, “Lacunary recurrence formulas for the numbers of Bernoulli and Euler,” Ann. Math. 36, No. 3, 637–649 (1935).
M. Merca, “On lacunary recurrences with gaps of length four and eight for the Bernoulli numbers,” Bull. Korean Math. Soc. 56, No. 2, 491–499 (2019).
K. A. Mirzoev and T. A. Safonova, “Green’s function of ordinary differential operators and an integral representation of sums of certain power series,” Dokl. Math. 98, No. 2, 486–489 (2018).
K. A. Mirzoev and T. A. Safonova, “Ordinary differential operators and the integral representation of sums of certain power series,” Trans. Mosc. Math. Soc. 2019, 133–151 (2019).
K. A. Mirzoev and T. A. Safonova, “Polynomials in the differentiation operator and formulas for the sums of certain convergent series,” Funct. Anal. Appl. 56, No. 1, 61–71 (2022).
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Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 87-94.
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Mirzoev, K.A., Safonova, T.A. Lacunary Recurrent Relations with Gaps of Length Four for the Bernoulli and Euler Polynomials. J Math Sci 270, 600–608 (2023). https://doi.org/10.1007/s10958-023-06371-8
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DOI: https://doi.org/10.1007/s10958-023-06371-8