Related papers: Some applications of the Beta function

This article deals with the ratio of normalized Mittag-Leffler function $\mathbb{E}_{\alpha,\beta}(z)$ and its sequence of partial sums $(\mathbb{E}_{\alpha,\beta})_m(z)$. Several examples which illustrate the validity of our results are…

The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.

This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

Some notes and observations on analytic functions defined on an annulus

We give a survey on eta invariants including methods of computation and applications in differential topology.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

This note contains a simple construction of complete sets of MUBs, using bent functions to write the new basis vectors as explicit linear combinations of the standard basis.

We deal with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and show some evidence to indicate the hypothesis in this note.

In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional…

We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.

In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.

We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a…

We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.

We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations,…

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the…

The association of subordination and special functions is used to find sharp estimates on the parameter $\beta$ such that the analytic function $p(z)$ is subordinate to certain functions having positive real part whenever $p(z)+\beta z…

In this study, we obtain some convexity, monotonicity and additivity properties as well as some inequalities involving the Nielsen's $\beta$-function which was introduced in 1906.

Memoir on the Sigma invariants and their applications, version 2