Extended Hypergeometric Functions and Orthogonal Polynomials
- 1st Edition - February 1, 2026
- Latest edition
- Editors: Praveen Agarwal, Clemente Cesarano
- Language: English
Extended Hypergeometric Functions and Orthogonal Polynomials presents a comprehensive and accessible resource for researchers and graduate students interested in exploring the ri… Read more
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
Researchers, graduate students, and professionals working in the fields of applied mathematics, statistics, engineering, physics, and computer science
Acknowledgment
About The Editor
Introduction
1. Generalized $k$ type-hypergeometric functions as the Meijer G-function
2. Matrix analogue of new class of hypergeometric function
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 U–Bernoulli 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
About The Editor
Introduction
1. Generalized $k$ type-hypergeometric functions as the Meijer G-function
2. Matrix analogue of new class of hypergeometric function
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 U–Bernoulli 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
- Edition: 1
- Latest edition
- Published: February 1, 2026
- Language: English
PA
Praveen Agarwal
Dr. Praveen Agarwal is Vice-Principal and Professor at Anand International College of Engineering, Jaipur, India. He is listed as the World's Top 2% Scientist in 2020, 2021, 2022, and 2023, released by Stanford University. In the 2023 ranking of best scientists worldwide announced by Research.com, he ranked 21st at the India level and 2436th worldwide in Mathematics. He is a Managing Editor of Book seriesMathematics for Sustainable Developments, Springer Nature,and Editor ofBook series Mathematical Modelling & Computational Method for Innovation, Taylor & Francis Group.
He published more than 350 papers in international reputed Journals.
Affiliations and expertise
Full Professor, Anand International College of Engineering, Jaipur India; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE; Peoples Friendship University of Russia (RUDN University), Russian FederationCC
Clemente Cesarano
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.
Affiliations and expertise
International Telematic University, Uninettuno, Rome, Italy