Related papers: Some New Results for Generalized Incomplete Expone…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
By applying an integral representation for $q^{k^{2}}$ we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of $q$-functions and polynomials that…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric…
Generalized integral formulas involving the generalized modified k-Bessel function $J_{k,\nu }^{c,\gamma ,\lambda }\left( z\right) $ of first kind are expressed in terms generalized $k-$Wright functions. Some interesting special cases of…
In this work, series expansions in terms of Bessel functions of the first kind are given for the sine and cosine integrals. These representations differ from many of the known Neumann-type series expansions for the sine and cosine…
We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm,…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…
The derivatives with respect to order {\nu} for the Bessel functions of argument x (real or complex) are studied. Representations are derived in terms of integrals that involve the products pairs of Bessel functions, and in turn series…
Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…
Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
A new generalization of the modified Bessel function of the second kind $K_{z}(x)$ is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby…
The modified q-Bessel functions and the q-Bessel-Macdonald functions of the first and second kind are introduced. Their definition is based on representations as power series. Recurrence relations, the q-Wronskians, asymptotic…
In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…