Related papers: Monotonicity properties of some Dini functions
In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…
The introduction of a fractional differential operator defined in terms of the Riemann-Liouville derivative makes it possible to generalize the kinetic equations used to model relaxation in dielectrics. In this context such fractional…
In this paper two identities involving a function defined by the complete elliptic integrals of the first and second kinds are proved. Some functional inequalities and elementary estimates for this function are also derived from the…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
In this paper a necessary and sufficient condition is deduced for the close-to-convexity of a cross product of Bessel and modified Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about…
In this note we prove a condition of monotonicity for the integral functional $ F(g) = \int_a^b h(x)\, d[-g(x)] $ with respect to $g$, a function of bounded variation. This condition is applied to analyze the behavior of a generalized…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…
Tur\'an, Mitrinovi\'c-Adamovi\'c and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag-Leffler expansion for the regular Coulomb wave function, which may be of independent interest.…
The Mittag-Leffler function $E_{\alpha}$ being a natural generalization of the exponential function, an infinite-dimensional version of the fractional Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)…
The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of…
The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of…
In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are…
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform…
A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order, and are not necessarily smooth. We show that such functions have a unique integral…
We review the function theoretical properties of the Mittag-Leffler function $E_{a,b}\left( z\right) $ in a self-contained manner, but also add new results; more than half is new!
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…
Let $ f:(0,\infty)\rightarrow \Bbb{R} $ be a completely monotonic function. In this paper, we present some properties of this functions and several new classes of completely monotonic functions. We also give some special functions such that…
The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include…
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional…