The Umbral Calculus Book

	Preface	ix
Chapter 1	Introduction
1	A Definition of the Classical Umbral Calculus	1
2	Preliminaries	3
Chapter 2	Sheffer Sequences
1	The Umbral Algebra	6
2	Linear Operators	12
3	Sheffer Sequences	17
4	Associated Sequences	25
5	Appell Sequences	26
6	A Few Examples	28
Chapter 3	Operators and Their Adjoints
1	Continuous Operators on P*	32
2	Automorphisms and Derivations on P*	33
3	Adjoints	34
4	Umbral Operators and Umbral Composition	37
5	Sheffer Operators and Umbral Composition	42
6	Umbral Shifts and the Recurrence Formula for Associated Sequences	45
7	Sheffer Shifts and the Recurrence Formula for Sheffer Sequences	49
8	The Transfer Formulas	50
Chapter 4	Examples
1	Associated Sequences	53
2	Appell Sequences	86
3	Sheffer Sequences	107
4	Other Sheffer Sequences	125
Chapter 5	Topics
1	The Connection Constants Problem and Duplication Formulas	131
2	The Lagrange Inversion Formula	138
3	Cross Sequences and Steffensen Sequences	140
4	Operational Formulas	144
5	Inverse Relations	147
6	Sheffer Sequence Solutions to Recurrence Relations	156
7	Binomial Convolution	160
Chapter 6	Nonclassical Umbral Calculi
1	Introduction	162
2	The Principal Results	162
3	A Particular Delta Series and the Gegenbauer Polynomials	166
4	The q-Umbral Calculus	174
	References	183
	Index	189