Reciprocal relations of Bernoulli and Euler numbers/polynomials. (English) Zbl 1397.11055
Summary: By means of the symmetric summation theorem on polynomial differences due to the second author and P. Magli [Eur. J. Comb. 28, No. 3, 921–930 (2007; Zbl 1125.05012)], we examine Bernoulli and Euler polynomials of higher order. Several reciprocal relations on Bernoulli and Euler numbers and polynomials are established, including some recent ones obtained by T. Agoh [J. Number Theory 176, 149–173 (2017; Zbl 1422.11038)].
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
Keywords:
Bernoulli number and polynomial; Euler number and polynomial; incomplete beta function; recurrence relation; reciprocal relationReferences:
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