Generalized Bessel Functions of the First Kind
In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these gene
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1994
Árpád Baricz
Generalized Bessel Functions of the First Kind
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Árpád Baricz Babes-Bolyai University Department of Economics Cluj-Napoca 400084 Romania [email protected]
ISBN: 978-3-642-12229-3 e-ISBN: 978-3-642-12230-9 DOI: 10.1007/978-3-642-12230-9 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2010926688 Mathematics Subject Classification (2000): 33C05, 33C10, 33C15, 33C75, 30C45, 26D05, 26D07, 39B62 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: SPi Publisher Services Printed on acid-free paper springer.com
Dedicated to my children Bor´oka and Kopp´any
Preface
Bessel functions are indispensable in many branches of mathematics and applied mathematics. Thus, it is important to study their properties in many aspects. Recently, there has been a vivid interest on Bessel and hypergeometric functions from the point of view of geometric function theory and functional inequalities. Although many inequalities and geometric properties of Bessel and hypergeometric functions appear in works of many mathematicians, there is no unified treatment of the topic. I have written this monograph in order to partially fill this gap in the literature. The major part of this monograph is taken from my Ph.D. thesis [54] with the same title as this monograph and that is why most results are due to myself and my coauthors. The literature has grown very quickly during the past few years and everything could not have been covered. I have tried to follow closely the structure of my thesis. Most of my papers used in this monograph were supported partially by the Institute of Mathematics, University of Debrecen, Hungary and some of these papers were completed during my visit to University of Debrecen. I take this opportunity to thank this institution for its excellent research facilities and to thank P´eter T. Nagy for his constant encouragement during the course of my work. My research was also partially supported by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences since September 2009. I would also like to thank this Instit
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