Description
Extended Hypergeometric Functions and Orthogonal Polynomials presents a comprehensive and accessible resource for researchers and graduate students interested in exploring the rich connections between extended hypergeometric functions, orthogonal polynomials, and multivariable polynomials. Integrating all three fields and their applications in Maple, Mathematica, and MATLAB, this book fosters interdisciplinary understanding and inspires new avenues of research in mathematics, engineering, physics, and computer science. It also provides a glimpse into future research directions in these areas, including potential applications in emerging fields of applied mathematics and interdisciplinary collaborations. Each chapter begins with an introduction, includes sections on theory, followed by sections on applications, and ends with exercises, problems, references and suggested readings.- Provides an integrated and up-to-date resource on extended hypergeometric functions, orthogonal polynomials, and multivariable polynomials for researchers, students, and practicing engineers- Presents emerging trends, new developments, techniques, and applications in the fields of special functions and orthogonal polynomials- Gives special attention to practical techniques for working with these functions and polynomials, including computational methods and applications to solve real-world problems
Table of Contents
1. Generalized $k$ type-hypergeometric functions as the Meijer G-function2. Matrix analogue of new class of hypergeometric function3. Some extended type hypergeometric functions of two and three variables4. AN EXTENSION OF k-GAMMA AND k-BETA MATRIX FUNCTION BY USE OF TWO PARAMETER k-MITTAG-LEFFLER FUNCTION5. $k$-TYPE CAPUTO FRACTIONAL DERIVATIVE OPERATOR AND ITS PROPERTIES6. AN EXTENSION OF k-HYPERGEOMETRIC FUNCTIONS7. Certain Pathway Fractional Integral Formulae Involving Extended $k$-Hypergeometric Functions.8. Certain integral transforms for the k- hypergeometric function9. Generalized Riemann- Liouville k- fractional derivative and its properties10. Main Results on U–Bernoulli Korobov-type polynomials and their Approximate Roots11. Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients12. Inverse problem for the loaded heat conductivity equation with variable coefficients13. Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators14. Fractional Integration and Differentiation of the Generalized Arbitrary Order Mittag-Leffler-Type Function15. Generalized Fractional Order Kinetic Equations Involving Multi-Index Mittag-Leffler Function of Several Variables16. Certain Integrals Involving $k$-type $R$- and $G$-Functions17. Fractional Integrals and Solution of Fractional Kinetic Equations involving R-and G-Functions
