Junesang Choi

Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity.MSC:11M06, 33B15, 33E20, 11M35, 11M41, 40C15.

Contiguous Extensions of Dixon's Theorem on the Sum of a

In 1994, Lavoie et al. have succeeded in artificially constructing a formula consisting of twenty three interesting results, except for five cases, closely related to the classical Dixons theorem on the sum of a by making a systematic use of some known relations among contiguous functions. We aim at presenting summation formulas for those five exceptional cases that can be derived by using the same technique developed by Bailey with the help of Gausss summation theorem and generalized Kummers theorem.

Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function

Many useful and interesting properties, identities, and relations for the Riemann zeta function ζ(s) and the Hurwitz zeta function ζ(s,a) have been developed. Here, we aim at giving certain (presumably) new and (potentially) useful relationships among polygamma functions, Riemann zeta function, and generalized zeta function by modifying Chen’s method. We also present a double inequality approximating ζ(2r+1) by a more rapidly convergent series.MSC:11M06, 33B15, 40A05, 26D07.

Certain integral representations of Stieltjes constants γ n

A remarkably large number of integral formulas for the Euler-Mascheroni constant γ have been presented. The Stieltjes constants (or generalized Euler-Mascheroni constants) γn and γ0=γ, which arise from the coefficients of the Laurent series expansion of the Riemann zeta function ζ(s) at s=1, have been investigated in various ways, especially for their integral representations. Here we aim at presenting certain integral representations for γn by choosing to use three known integral representations for the Riemann zeta function ζ(s). Our method used here is similar to those in some earlier works, but our results seem a little simpler. Some relevant connections of some special cases of our results presented here with those in earlier works are also pointed out.MSC:11M06, 11M35, 11Y60, 33B15.

Certain inequalities involving the k-Struve function

We aim to introduce a k-Struve function and investigate its various properties, including mainly certain inequalities associated with this function. One of the inequalities given here is pointed out to be related to the so-called classical Turán-type inequality. We also present a differential equation, several recurrence relations, and integral representations for this k-Struve function.