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.
1. Generalized $k$ type-hypergeometric functions as the Meijer
G-function
2. Matrixanalogueofnewclassofhypergeometricfunction
3. Some extended type hypergeometric functions of two and three variables
4. AN EXTENSION OF k-GAMMA AND k-BETA MATRIX FUNCTION BY USE OF TWO PARAMETER
k-MITTAG-LEFFLER FUNCTION
5. $k$-TYPE CAPUTO FRACTIONAL DERIVATIVE OPERATOR AND ITS PROPERTIES
6. AN EXTENSION OF k-HYPERGEOMETRIC FUNCTIONS
7. Certain Pathway Fractional Integral Formulae Involving Extended
$k$-Hypergeometric Functions.
8. Certain integral transforms for the k- hypergeometric function
9. Generalized Riemann- Liouville k- fractional derivative and its
properties
10. Main Results on UBernoulli Korobov-type polynomials and their
Approximate Roots
11. Solvability of the Cauchy problem for a fractionally loaded equation with
variable coefficients
12. Inverse problem for the loaded heat conductivity equation with variable
coefficients
13. Generalized arbitrary order Mittag-Leffler-type function and
Marichev-Saigo-Maeda fractional operators
14. Fractional Integration and Differentiation of the Generalized Arbitrary
Order Mittag-Leffler-Type Function
15. Generalized Fractional Order Kinetic Equations Involving Multi-Index
Mittag-Leffler Function of Several Variables
16. Certain Integrals Involving $k$-type $R$- and $G$-Functions
17. Fractional Integrals and Solution of Fractional Kinetic Equations
involving R-and G-Functions
Dr. Praveen Agarwal earned his Ph. D. in Mathematics at the Malviya National Institute of Technology (MNIT) in Jaipur, India, in 2006. Recently, Prof. Agarwal has been listed as the World's Top 2% Scientist from 2020-2025, released by Stanford University. In the 2025 ranking of best scientists worldwide announced by Research.com, he ranked 13th at the India level and 1297th worldwide in Mathematics. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 24 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, Probability & Statistics, and Fixed Point Theorems. He has published 11 research monographs and edited volumes and more than 405 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia and Thailand. He has served over 50 Journals in the capacity of an Editor/Honorary Editor, or Associate Editor, and published 15 books as an editor. Clemente Cesarano is an associate professor of numerical analysis at the UNINETTUNO University, where he coordinates the local mathematics section and the doctoral course in technological innovation engineering. He has carried out teaching and research activities in various Italian and European institutions and universities; he has been a visiting professor in some European universities, including the University of Linz and the Complutense University of Madrid. He is the author of over 200 scientific publications texts and manuals in the field of approximation theory and mathematical analysis. He has participated, also as coordinator, in various national and international funded research projects.
