Bessel Polynomials
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698 Emil Grosswald
Bessel Polynomials I ~ ~·
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Springer-Verlag Berlin Heidelberg New York 1978
Author
Emil Grosswald Department of Mathematics Temple University Philadelphia, PA 19122/USA
AMS Subject Classifications (1970): primary: 33A 70 secondary: 33A65, 33A40, 33A 75, 33A45, 33-01,33-02,33-03, 35J05, 41A10, 44A10, 30A22, 30A80. 30A84,10F35,12A20,12D10, 60E05 ISBN ISBN
3-540-09104-1 0-38 7-09104 -1
Springer-Verlag Berlin Heidelberg New York Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved. whether the whole or part of the matenal is concerned, specifically those of translation, reprinting. re-use of illustrations, broadcasting. reproduction by photocopying machine or similar means, and storage in data banks. Under§ 54 of the German Copynght Law where copies are made for other than private use. a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. ·:C by Springer-Verlag Berlin Heidelberg 1978 Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
To ELIZABETH
BLANCHE . .
and
VIVIAN
FOREWORD The present book consists of an Introduction, 15 Chapters, an Appendix, two Bibliographies and two Indexes. The chapters are numbered consecutively, from 1 to 15 and are grouped into four parts, as follows: Part I
- A short historic sketch (1 Chapter) followed by the basic theory
(3 Chapters); Part II
-Analytic properties (5 Chapters);
Part III -Algebraic properties (4 Chapters); Part IV
- Applications and miscellanea (2 Chapters).
According to its subject matter, the chapter on asymptotic properties would fit better into Part II; however, some of the proofs require results obtained only in Chapter 10 (properties of zeros) and, for that reason, the chapter has been incorporated into Part III. The Appendix contains a list of some 12 open problems. In the first bibliography are listed all papers, monographs, etc., that could be located and that discuss Bessel Polynomials.
It is quite likely that, despite
all efforts made, absolute completeness has not been achieved.
The present writer
takes this opportunity to apologize to all authors, whose work has been overlooked. A second, separate bibliography lists books and papers
quote~
in the text, but
not directly related to Bessel Polynomials. References to the bibliographies are enclosed in square brackets. ing to the second bibliography are distinguished by heavy print. W.H. Abdi - A basic analog of the Bessel Polynomials; while
[~]
Those refer-
So (1] refers to: refers to: M. Abramo-
witz and I.E. Segun - Handbook of Mathematical Functions. Within each chapter, the sections, theorems, lemmata, corollaries, drawings, and formulae are numbered consecutively.
If quoted, or referred to within the same
chapter, only their own number is mentioned.
If, e.g., in Chapter 10 a reference
is made to formula (12), or to Section 2, this means formula (12), or Section 2 of Chapter 10.
The same formula, or
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