ISSN 2394-5125
 

Research Article 


Bernoulli Polynomials and Riemann Zeta Function

Dr. R. Sivaraman.

Abstract
Ever since Swiss mathematician Jacob Bernoulli published his work about “Bernoulli Numbers” in 1713, there have
been great amount of work done regarding it. In this paper, we try to generalize the Bernoulli numbers to class of
polynomials called Bernoulli Polynomials. In particular, we see that the constant terms of Bernoulli polynomials are
precisely the Bernoulli numbers. After introducing Bernoulli numbers and Bernoulli polynomials we discuss a
property of Bernoulli polynomials through which the relation between Bernoulli Polynomials and Riemann Zeta
Function is obtained. We also deduce an important result regarding Riemann Zeta Function.

Key words: Bernoulli Numbers, Bernoulli Polynomials, Generating Functions, Riemann Zeta Function, Trivial zeros.


 
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Pubmed Style

Dr. R. Sivaraman. Bernoulli Polynomials and Riemann Zeta Function. JCR. 2020; 7(17): 1253-1260. doi:10.31838/jcr.07.17.160


Web Style

Dr. R. Sivaraman. Bernoulli Polynomials and Riemann Zeta Function. http://www.jcreview.com/?mno=29159 [Access: April 15, 2021]. doi:10.31838/jcr.07.17.160


AMA (American Medical Association) Style

Dr. R. Sivaraman. Bernoulli Polynomials and Riemann Zeta Function. JCR. 2020; 7(17): 1253-1260. doi:10.31838/jcr.07.17.160



Vancouver/ICMJE Style

Dr. R. Sivaraman. Bernoulli Polynomials and Riemann Zeta Function. JCR. (2020), [cited April 15, 2021]; 7(17): 1253-1260. doi:10.31838/jcr.07.17.160



Harvard Style

Dr. R. Sivaraman (2020) Bernoulli Polynomials and Riemann Zeta Function. JCR, 7 (17), 1253-1260. doi:10.31838/jcr.07.17.160



Turabian Style

Dr. R. Sivaraman. 2020. Bernoulli Polynomials and Riemann Zeta Function. Journal of Critical Reviews, 7 (17), 1253-1260. doi:10.31838/jcr.07.17.160



Chicago Style

Dr. R. Sivaraman. "Bernoulli Polynomials and Riemann Zeta Function." Journal of Critical Reviews 7 (2020), 1253-1260. doi:10.31838/jcr.07.17.160



MLA (The Modern Language Association) Style

Dr. R. Sivaraman. "Bernoulli Polynomials and Riemann Zeta Function." Journal of Critical Reviews 7.17 (2020), 1253-1260. Print. doi:10.31838/jcr.07.17.160



APA (American Psychological Association) Style

Dr. R. Sivaraman (2020) Bernoulli Polynomials and Riemann Zeta Function. Journal of Critical Reviews, 7 (17), 1253-1260. doi:10.31838/jcr.07.17.160