The Umbral Calculus
Published on 21. March 1984
192 pages
978-0-08-087430-2 (ISBN)
Description
The Umbral Calculus
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Steven Roman
Umbral Calculus
Book
01/1984
Academic Press
€75.64
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Content
- Front Cover
- The Umbral Calculus
- Copyright Page
- Contents
- Preface
- CHAPTER 1. INTRODUCTION
- 1. A Definition of the Classical Umbral Calculus
- 2. Preliminaries
- CHAPTER 2. SHEFFER SEQUENCES
- 1. The Umbral Algebra
- 2. Linear Operators
- 3. Sheffer Sequences
- 4. Associated Sequences
- 5. Appell Sequences
- 6. A Few Examples
- CHAPTER 3. OPERATORS AND THEIR ADJOINTS
- 1. Continuous Operators on P*
- 2. Automorphisms and Derivations on P*
- 3. Adjoints
- 4. Umbral Operators and Umbral Composition
- 5. Sheffer Operators and Umbral Composition
- 6. Umbral Shifts and the Recurrence Formula for Associated Sequences
- 7. Sheffer Shifts and the Recurrence Formula for Sheffer Sequences
- 8. The Transfer Formulas
- CHAPTER 4. EXAMPLES
- 1. Associated Sequences
- 2. Appell Sequences
- 3. Sheffer Sequences
- 4. Other Shefi'er Sequences
- CHAPTER 5. TOPICS
- 1. The Connection Constants Problem and Duplication Formulas
- 2. The Lagrange Inversion Formula
- 3. Cross Sequences and Steffensen Sequences
- 4. Operational Formulas
- 5. Inverse Relations
- 6. Sheffer Sequence Solutions to Recurrence Relations
- 7. Binomial Convolution
- CHAPTER 6. NONCLASSICAL UMBRAL CALCULI
- 1. Introduction
- 2. The Principal Results
- 3. A Particular Delta Series and the Gegenbauer Polynomials
- 4. The q-Umbra1 Calculus
- REFERENCES
- Index
