UID:
almahu_9947367196302882
Format:
1 online resource (207 p.)
ISBN:
1-281-76888-X
,
9786611768881
,
0-08-087430-4
Series Statement:
Pure and applied mathematics ; 111
Content:
The umbral calculus
Note:
Description based upon print version of record.
,
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
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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
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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
,
English
Additional Edition:
ISBN 0-12-594380-6
Language:
English
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