arXiv subjects

Akerele Olofin Segun

Publications and source records attributed to Akerele Olofin Segun.

3 recordsLinked to original sources

arXiv2024

Some Classes of series involving the Riemann zeta function, Fibonacci numbers and the Lucas numbers

The objective of this manuscript is to offer explicit expressions for diverse categories of infinite series incorporating the Fibonacci (Lucas) sequence and the Riemann zeta function. In demonstrating our findings, we will utilize conventional methodologies and integrate the Binet formulas pertinent to these sequences with generating functions that encompass the Riemann zeta function alongside established evaluations of certain series.

math.GM↗

arXiv2024

Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\binom{2n}{n}$

We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward transformation to obtain new evaluations linked to Fibonacci numbers and the golden ratio. Before the end of this paper, we also gave a new series representation for $ζ(2)$.

math.NT↗

arXiv2024

Riemann Integration in the Euclidean Space

The so-called Riemann sums have their origin in the efforts of Greek mathematicians to find the center of gravity or the volume of a solid body. These researches led to the method of exhaustion, discovered by Archimedes and described using modern ideas by MacLaurin in his \textit{Treatise of Fluxions} in 1742. At this times the sums were only a practical method for computing an area under a curve, and the existence of this area was considered geometrically obvious. The method of exhaustion consists in almost covering the space enclosed by the curve with $n$ geometric objects with well-known areas such as rectangles or triangles, and finding the limit (though this topic was very blurry at these early times) when $n$ increases. One of its most remarkable application is squaring the area $\mathcal{A}$ enclosed by a parabola and a line.

math.HO↗