Open Access Open Access  Restricted Access Subscription Access

Binomially Regularized Riemann Zeta Function

Lukasz Andrzej Glinka


In this article, the most essential part of the binomial regularization of the Riemann zeta function, initiated through the author in an earlier book, is presented. The idea of the method arises from convergence of the negative binomial series determined in the standard sense of the infinite series theory. Meanwhile, the obtained result involves a remarkable series expansion of the Riemann zeta function in terms of the generalized Newton binomial coefficients and the Bernoulli polynomials which can be interesting from the point of view of further research of the Riemann zeta function and related problems, such like the Riemann hypothesis.


Cite this Article:
Lukasz Andrzej Glinka. Binomially Regularized Riemann Zeta Function. Research & Reviews: Discrete Mathematical Structures. 2015; 2(1): 1–8p.


Riemann zeta function; regularization methods; generalized Newton binomial coefficients; Taylor power series expansion; Bernoulli polynomials

Full Text:



Ferrar W.L. A Text-Book of Convergence. Oxford University Press; G.H. Hardy. 1938.

Divergent Series. Oxford University Press; K. Knopp. 1949.

Infinite Sequences and Series. Dover Publications;G.M. Fichtenholz. 1956.

Fichtenholz G.M. Infinite Series: Ramifications, Gordon & Breach. 1970. Trench W.F. Introduction to Real Analysis, Prentice Hall. 2002.

Graham L., Knuth D.E., and Patashnik O. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley. 1994.

Glinka L.A. Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions. Cambridge International Science Publishing.2014.


  • There are currently no refbacks.

This site has been shifted to