An identity of symmetry for the Bernoulli polynomials. (English) Zbl 1133.11015
The author proves an identity of symmetry for the higher Bernoulli polynomials. It turns out implies that the recurrence relation and multiplication theorem for the Bernoulli polynomials discussed by F. T. Howard [J. Number Theory 52, No. 1, 157–172 (1995; Zbl 0844.11019)], as well as a relation of symmetry between the power sum polynomials and the Bernoulli numbers developed by H. J. H Tuenter [Am. Math. Mon. 108, No. 3, 258–261 (2001; Zbl 0983.11008)], are special cases of the results in this paper.
Reviewer: Ping Sun (Shenyang)
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
Keywords:
Power sum polynomial; Bernoulli numbers; Bernoulli polynomial; Higher order Bernoulli polynomialsReferences:
| [1] | Comtet, L., Advanced Combinatories (1974), Reidel: Reidel Dordrecht |
| [2] | Deeba, E.; Rodriguez, D., Stirling’s series and Bernoulli numbers, Amer. Math. Monthly, 98, 423-426 (1991) · Zbl 0743.11012 |
| [3] | Gessel, I., Solution to problem E3237, Amer. Math. Monthly, 96, 364 (1989) |
| [4] | Howard, F. T., Application of a recurrence for the Bernoulli numbers, J. Number Theory, 52, 157-172 (1995) · Zbl 0844.11019 |
| [5] | Tuenter, H. J.H., A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly, 108, 258-261 (2001) · Zbl 0983.11008 |
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