On new extensions of the generalized Hermite matrix polynomials

Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of xnI, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae

An extension of basic Humbert hypergeometric functions

Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain interesting several $q$-partial derivative formulas, $q$-contiguous function relations, $q$-recurrence relations, various $q$-partial differential equations, summation formulas, transformation formulas and $q$-integrals representations for basic Humbert confluent hypergeometric functions under what constraints of parameters. These interesting properties, as special cases, include many known expansions of basic Humbert hypergeometric functions, and are also include particular interest in the area

Some relations on generalized Rice\u27s matrix polynomials

The main aim of this paper is to obtain certain properties of generalized Rice’s matrix polynomials such as their matrix differential equation, generating matrix functions, an expansion for them. We have also deduced the various families of bilinear and bilateral generating matrix functions for them with the help of the generating matrix functions developed in the paper and some of their applications have also been presented here

On q-Horn hypergeometric functions H6\mathbf{H}_6 and H7\mathbf{H}_7

The aim of this work is to construct various interesting properties for basic Horn functions $\mathbf{H}_6$ and $\mathbf{H}_7$ under conditions on the denominator parameters, such as several $q$-contiguous function relations, $q$-differential relations, and $q$-differential equations. Special cases of our main results are also demonstrated

Some relations satisfied by Hermite-Hermite matrix polynomials

summary:The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials

On certain new formulas for the Horn's hypergeometric functions G1\mathcal{G}_{1}, G2\mathcal{G}_{2} and G3\mathcal{G}_{3}

Inspired by the recent work Sahin and Agha gave recursion formulas for $\mathcal{G}_{1}$ and $\mathcal{G}_{2}$ Horn hypergeometric functions \cite{saa}. The object of work is to establish several new recursion relations, relevant differential recursion formulas, new integral operators, infinite summations and interesting results for Horn's hypergeometric functions $\mathcal{G}_{1}$, $\mathcal{G}_{2}$ and $\mathcal{G}_{3}$

Awareness, attitude and preference of long-acting reversible contraceptives by Tanta University contraceptive clinic attendants

Background: Long Acting Reversible Contraceptives (LARC) had a very high efficacy in lowering unintended pregnancies and their poor health sequalae. Although their reported efficacy, these methods are not widely used among patient’s due to non-awareness and faulty concepts linked to these methods.Methods: This cross-sectional study was conducted to determine the degree of awareness, attitude and preference of LARC by attendants of Tanta University contraceptive clinic in the period from January 1, 2016 to December 31, 2016. All patients were counseled with thorough discussion about LARC methods. The following issues were determined: age, parity, mode of previous delivery, residence, medical diseases, socioeconomic state of family, type of LARC method used, how she know about this method and why she preferred that type.Results: 391 women underwent this study with age range of 21-46 years, and BMI range of 20.46-31.87. LARC were preferred by 72.38% of patients and mainly IUDS (52.94%) while other LARC methods were of very low awareness. Most patients take their knowledge from paramedical staffs (49.87%). Occupation, education, residence and religion were not affecting patients' attitude and preference of one LARC over the other methods. Age was the most effective factor for determining whether to use LARC or not. Counseling revert a lot of faulty concepts and misbelieves about LARC.Conclusions: LARC were not widespread among Tanta University attendants for contraception except for IUDs. Young patients had no motivations towards LARC due to a lot of faulty concepts that need a lot of work to be eradicated

Associated Matrix Polynomials with the Second Kind Chebyshev Matrix Polynomials

This paper deals with the study of the associated Chebyshev matrix polynomials. Associated matrix polynomials with the Chebyshev matrix polynomials are defined here. Some properties of the associated Chebyshev matrix polynomials are obtained here. Further, we prove that the associated Chebyshev matrix polynomials satisfy a matrix differential equation of the second order

On incomplete exponential \;_{r}R_{s}(P,Q,z) matrix function

The recurrence matrix relations, differentiation formulas, and analytical and fractional integral properties of incomplete gamma matrix functions $\gamma(Q, x)$ and $\Gamma(Q, x)$ are all covered in this article. The generalized incomplete exponential matrix functions with their integral representations functions have been examined, along with some relevant characteristics of these functions such as integral representations functions . Additionally, the infinite summation relations and formulas for two sequences are shown, along with the generalized incomplete exponential matrix functions with the integral representation, addition formula for addition of two arguments, multiplication formula for multiplication of two arguments, and recurrence matrix relation