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. Introduction to Extended Hypergeometric Functions and Orthogonal Polynomials: Definitions and Overview
2. Generalizations and Extended Hypergeometric Functions and their implementation via Maple
3. Generalizations and Extended Hypergeometric Functions and their implementation via Mathematica
4. Generalizations and Extended Hypergeometric Functions and their implementation via MATLAB
5. Generalized and Extended Orthogonal Polynomials their implementation via Maple
6. Generalized and Extended Orthogonal Polynomials their implementation via Mathematica
7. Generalized and Extended Orthogonal Polynomials their implementation via MATLAB
8. q-analogue of extended hypergeometric functions
9. q-analogue of Orthogonal Polynomials
10. Multivariable Polynomials and their implementation via Maple/ Mathematica/ MATLAB
11. Applications in mathematical physics
12. Applications in quantum mechanics and wave equations
13. Applications in classical mechanics and special functions
14. Applications in statistical mechanics and random matrices
15. Applications in probability and Statistics, computational aspects
16. Advance Topics and Future Directions in applications of Hypergeometric Functions
17. Advance Topics and Future Directions in applications of Orthogonal Polynomials
18. Advance Topics and Future Directions in applications of Multivariable Polynomials
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