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The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss’s multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are spe- cial cases of the results presented in this paper, including Tuenter’s classi- cal results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258– 261] and D. S. Kim’s eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math.
Appl. 60 (2010), no. 8, 2350–2359].
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참고문헌 (35)
참고문헌 신청
Z. W. Sun / Introduction to Bernoulli and Euler polynomials
B. A. Tangedal / 2011 / On p-adic multiple zeta and log gamma functions / J. Number Theory 131(7):1240~1257
L. Tao / 2004 / A reciprocity law for uniform functions / Nanjing Univ. J. Math. Biquarterly 21(2):201~205
H. J. H. Tuenter / 2001 / A symmetry of power sum polynomials and Bernoulli numbers / Amer. Math. Monthly 108(3):258~261
W. Wang / 2010 / Some results on power sums and Apostol-type polynomials / Integral Transforms Spec. Funct 21(3-4):307~318
B. A. Tangedal / 2011 / On p-adic multiple zeta and log gamma functions / J. Number Theory 131(7):1240~1257
L. Tao / 2004 / A reciprocity law for uniform functions / Nanjing Univ. J. Math. Biquarterly 21(2):201~205
H. J. H. Tuenter / 2001 / A symmetry of power sum polynomials and Bernoulli numbers / Amer. Math. Monthly 108(3):258~261
W. Wang / 2010 / Some results on power sums and Apostol-type polynomials / Integral Transforms Spec. Funct 21(3-4):307~318
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