Related papers: Some relations between certain classes of analytic…

In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…

In the present article, we define a new subclass of pseudo-type meromorphic bi-univalent functions class $\Sigma'$ of complex order $\gamma \in \mathbb{C}\backslash \{0\}$ and investigate the initial coefficient estimates $|b_0|, |b_1|$ and…

Let $$\lambda(s)=\sum_{n=0}^\infty\frac1{(2n+1)^s},$$ $$\beta(s)=\sum_{n=0}^\infty\frac{(-1)^{n}}{(2n+1)^s},$$ and $$\eta(s)=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{n^s}$$ be the Dirichlet lambda function, its alternating form, and the Dirichlet…

This note introduces a new range of modified gamma and beta $k$ functions. The authors present new modified gamma and beta $k$-functions, first and second summation relations, various functionals, Mellin transforms, and integral…

Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…

Let $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ be the class of normalized analytic functions $f$ defined in the domain $|z|<1$ satisfying \begin{align*} {\rm Re\,}…

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$ of analytic and univalent functions in the open…

Let P(n) denote the largest prime factor of $n \ge 2, P(1) = 1$, and let $$ \beta(n) = \sum_{p|n}p, \Beta(n) = \sum_{p^\alpha||n}\alpha p, \Beta_1(n) = \sum_{\p^\alpha||n}p^\alpha $$ denote "large" additive functions. A survey of results on…

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…

In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $\zeta_\lambda$, zeta differences of first kind $\Delta_\lambda$ and second kind $\Delta_{\lambda,\mu}$ where…

We derive several identities for the Hurwitz and Riemann zeta functions, the Gamma function, and Dirichlet $L$-functions. They involve a sequence of polynomials $\alpha_k(s)$ whose study was initiated in an earlier paper. The expansions…

We give closed-form expressions for the Dirichlet beta function at even positive integers and for the Dirichlet lambda function at odd positive integers, based on the function J(s) defined via convergent integral. We also show fundamental…

In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…

We study the interplay between recurrences for zeta related functions at integer values, `Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and…

We study a certain class of arithmetic functions that appeared in Klurman's classification of $\pm 1$ multiplicative functions with bounded partial sums, c.f., Comp. Math. 153 (8), 2017, pp. 1622-1657. These functions are periodic and…

For $\alpha\geq 0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}(\alpha,\gamma)$ satisfies the condition \begin{align*} {\rm Re\,} \left( e^{i\phi}\left((1-\alpha+2\gamma)f/z+(\alpha-2\gamma)f'+ \gamma…

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…

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…

Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…

The classical beta function B(x; y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta…