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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.
MSC:
11B68Bernoulli and Euler numbers and polynomials
References:
[1]Comtet, L.: Advanced combinatories, (1974)
[2]Deeba, E.; Rodriguez, D.: Stirling’s series and Bernoulli numbers, Amer. math. Monthly 98, 423-426 (1991) · Zbl 0743.11012 · doi:10.2307/2323860
[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 · doi:10.1006/jnth.1995.1062
[5]Tuenter, H. J. H.: A symmetry of power sum polynomials and Bernoulli numbers, Amer. math. Monthly 108, 258-261 (2001) · Zbl 0983.11008 · doi:10.2307/2695389