Focusing on an algorithmic approach, this textbook serves as a comprehensive guide to computer algebra. The author, a leading expert, provides hands-on tutorials that promote practical skills and algorithmic thinking. This implementation-oriented method equips readers with versatile tools applicable in mathematical theory, various applications, and educational settings, making it a valuable resource for both students and educators.
An Algorithmic Approach to Summation and Special Function Identities
Focusing on modern algorithmic techniques for summation, this book explores advancements primarily from the 1990s. It provides detailed implementations within the Maple(TM) computer algebra system, offering readers insights into both theoretical concepts and practical applications in computational mathematics.
The Gamma Function - Hypergeometric Identities - Hypergeometric Database - Holonomic Recurrence Equations - Gosper's Algorithm - The Wilf-Zeilberger Method - Zeilberger's Algorithm - Extensions of the Algorithms - Petkovsek's Algorithm - Differential Equations for Sums - Differential Antiderivatives -Hyperexponential Antiderivatives - Holonomic Equations for Integrals - Rodrigues Formulas and Generating Functions