Binomially Regularized Riemann Zeta Function
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.
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.
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