• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.145-157
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• 2020

In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.1-16
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• 2006

In 1713, J. Bernoulli first discovered the method which one can produce those formulae for the sum $\sum\limits_{\iota=1}^{n}\;\iota^k$ for any natural numbers k ([5],[6]). In this paper, we investigate for the historical background and motivation of the sums of powers of consecutive integers due to J. Bernoulli. Finally, we introduce and discuss for the subjects which are studying related to these areas in the recent.