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Open AccessArticle

Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials

by 1,2,3,* and 4
1
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China
2
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China
3
Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387, China
4
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Mathematics 2016, 4(4), 65; https://doi.org/10.3390/math4040065
Received: 27 April 2016 / Revised: 8 November 2016 / Accepted: 17 November 2016 / Published: 24 November 2016
In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, and present several new recurrence relations for the Bernoulli numbers and polynomials. View Full-Text
Keywords: determinantal expression; recurrence relation; Bernoulli number; Bernoulli polynomial; Hessenberg determinant determinantal expression; recurrence relation; Bernoulli number; Bernoulli polynomial; Hessenberg determinant
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MDPI and ACS Style

Qi, F.; Guo, B.-N. Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials. Mathematics 2016, 4, 65. https://doi.org/10.3390/math4040065

AMA Style

Qi F, Guo B-N. Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials. Mathematics. 2016; 4(4):65. https://doi.org/10.3390/math4040065

Chicago/Turabian Style

Qi, Feng; Guo, Bai-Ni. 2016. "Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials" Mathematics 4, no. 4: 65. https://doi.org/10.3390/math4040065

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