Finite Calculus Associated with Bessel Functions

Finite Calculus Associated with Bessel Functions

by Frank M. Cholewinski
     
 

ISBN-10: 0821850830

ISBN-13: 9780821850831

Pub. Date: 12/31/1988

Publisher: American Mathematical Society

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

Overview

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 co-workers 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.

Product Details

ISBN-13:
9780821850831
Publisher:
American Mathematical Society
Publication date:
12/31/1988
Series:
Contemporary Mathematics Series, #75
Pages:
122
Product dimensions:
6.69(w) x 9.84(h) x (d)

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