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The Euler summation of numerical series
N. I. Dubrovin Vladimir State University, 87 Gorki str., Vladimir, 600000 Russia
Abstract:
A combinatorial equality was proved, which involves k-order differences and binomial coefficients as well. The Euler's summing of a sequence connects with calculation of all differences. Regularity of summing function means the coincidence with “ordinary” sum, if the last exists. As a consequence of proving combinatorial equality the simple proof of regularity Euler's summing was given.
Keywords:
summing of seriesies, Euler's summing, regularity of summing functions.
Received: 17.08.2019 Revised: 17.08.2019 Accepted: 25.09.2019
Citation:
N. I. Dubrovin, “The Euler summation of numerical series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 7, 76–82; Russian Math. (Iz. VUZ), 64:7 (2020), 66–72
Linking options:
https://www.mathnet.ru/eng/ivm9596 https://www.mathnet.ru/eng/ivm/y2020/i7/p76
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Abstract page: | 154 | Full-text PDF : | 87 | References: | 16 | First page: | 8 |
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