9 papers
Well-poised basic q-Taylor expansions with complementary remainders and a two-basis kernel
Abdulhafeez A. Abdulsalam, Michael J. Schlosser
We prove a nonterminating well-poised basic -Taylor expansion with complementary remainders for a two-basis infinite-product kernel implicitly proposed by the second author in \…
Signed Generalized Stirling Polynomials, Nested Sums, and Hyperbolic Secant Integral Identities
Abdulhafeez A. Abdulsalam, Michael J. Schlosser
We study signed generalized Stirling polynomials arising in closed forms for Malmsten-type hyperbolic secant integrals. Their product structure is used to prove recurren…
New identities for the Laplace transform and their applications
Abdulhafeez A. Abdulsalam, Ammar K. Mohammed
In this paper, we begin by applying the Laplace transform to derive closed forms for several challenging integrals that seem nearly impossible to evaluate. By utilizing the solutio…
Closed form for through the Hermite integral representation of the Hurwitz zeta function
Abdulhafeez A. Abdulsalam
Sums of positive integer powers have captivated the attention of mathematicians since ancient times. Over the centuries, mathematicians from diverse backgrounds have provided expre…
New closed forms for a dilogarithmic integral, related integrals, and series
Abdulhafeez A. Abdulsalam
In this study, we present a new closed form for the generalized integral where $a \in \mathbb{C} \setminus(-\infty,…
New closed forms for a class of digamma series and integrals
Abdulhafeez A. Abdulsalam
The pursuit of closed forms for infinite series has long been a focal point of research. In this paper, we contribute to this endeavor by presenting closed forms for the class of d…
An Alternate proof for a case of a Malmsten integral
Abdulhafeez Ayinde Abdulsalam
In this paper, a direct proof is presented for a case of a Malmsten integral. The method used in solving the integral is a direct one that the author has not come accross in any ol…
A new approach to evaluating Malmsten's integral and related integrals
Abdulhafeez A. Abdulsalam
This paper discusses generalizations of logarithmic and hyperbolic integrals. A new proof for an integral presented by Vardi and several other integrals in relation to known mathem…
New Integral Representations for the Bessel Functions
Abdulhafeez A. Abdulsalam, M. E. Egwe
In this paper, new integral representations for the Bessel and functions were presented and their results were used to derive an expression for the Modified Bessel func…