Contemporary Mathematics 1988; 122 pp; softcover Volume: 75 ISBN10: 0821850830 ISBN13: 9780821850831 List Price: US$29 Member Price: US$23.20 Order Code: CONM/75
 Although Bessel functions are among the most widely used functions in applied mathematics, this book is essentially the first to present a calculus associated with this class of functions. The author obtains a generalized umbral calculus associated with the Euler operator and its associated Bessel eigenfunctions for each positive value of an index parameter. For one particular value of this parameter, the functions and operators can be associated with the radial parts of \(n\)dimensional Euclidean space objects. Some of the results of this book are in part extensions of the work of Rota and his coworkers on the ordinary umbral calculus and binomial enumeration. The author also introduces a wide variety of new polynomial sequences together with their groups and semigroup compositional properties. Generalized Bernoulli, Euler, and Stirling numbers associated with Bessel functions and the corresponding classes of polynomials are also studied. The book is intended for mathematicians and physicists at the research level in special function theory. Table of Contents  The \(\nu\)umbral algebra
 The \(\nu\)umbral field
 The group of \(\nu\)delta functionals under composition
 Generalized binomial polynomial sequences
 The composition of polynomial sequences
 Compositions of Moebius delta functionals
 Generalized shift invariant operators
 The generalized derivative of \(\nu\)shift invariant operators
 Generalized Sheffer polynomials
 Cross sets of polynomials
 A class of Laguerre type polynomials
 The generalized heat polynomials
 A primitive integral for the Euler operator
 Bernoulli type polynomials and numbers
 Generalized Euler polynomials and numbers
 Generalized Stirling numbers and factor polynomials
