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The umbral calculus /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1984.
|
| Colección: | Pure and applied mathematics (Academic Press) ;
111. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- 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 Sequences7. 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 CALCULI1. Introduction; 2. The Principal Results; 3. A Particular Delta Series and the Gegenbauer Polynomials; 4. The q-Umbra1 Calculus; REFERENCES; Index