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El. knyga: Generalized Bessel Functions of the First Kind

  • Formatas: PDF+DRM
  • Serija: Lecture Notes in Mathematics 1994
  • Išleidimo metai: 17-Jun-2010
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783642122309
Kitos knygos pagal šią temą:
Generalized Bessel Functions of the First KindDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Lecture Notes in Mathematics 1994
  • Išleidimo metai: 17-Jun-2010
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783642122309
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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 generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.

This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.

Recenzijos

From the reviews:

In this book, which is based on the authors Ph.D. thesis with the same title the author studies the class B from several points of view. Approximately one-third of the book deals with questions related to or motivated by the classical theory of univalent functions. The style is very clear and carefully designed pictures facilitate the reading. interest for researchers of classical analysis working in the field of univalent function theory or inequalities for functions defined on the real axis. (Matti Vuorinen, Mathematical Reviews, Issue 2011 f)

1 Introduction and Preliminary Results
1(22)
1.1 Overview
1(6)
1.2 Generalized Bessel Functions of the First Kind
7(14)
1.3 Classical Inequalities
21(2)
2 Geometric Properties of Generalized Bessel Functions
23(48)
2.1 Univalence of Generalized Bessel Functions
23(16)
2.1.1 Sufficient Conditions Involving Jack's Lemma
26(2)
2.1.2 Sufficient Conditions Involving the Admissible Function Method
28(3)
2.1.3 Sufficient Conditions Involving the Alexander Transform
31(5)
2.1.4 Sufficient Conditions Involving Results of L. Fejer
36(3)
2.2 Starlikeness and Convexity Properties of Generalized Bessel Functions
39(18)
2.2.1 Sufficient Conditions Involving Jack's Lemma
39(2)
2.2.2 Sufficient Conditions Involving the Admissible Function Method
41(9)
2.2.3 Sufficient Conditions Involving Results of H. Silverman
50(5)
2.2.4 Close-to-Convexity with Respect to Certain Functions
55(2)
2.3 Applications Involving Bessel Functions Associated with Hardy Space of Analytic Functions
57(14)
2.3.1 Bessel Transforms and Hardy Space of Generalized Bessel Functions
58(4)
2.3.2 A Monotonicity Property of Generalized Bessel Functions
62(9)
3 Inequalities Involving Bessel and Hypergeometric Functions
71(116)
3.1 Functional Inequalities Involving Quotients of Some Special Functions
73(12)
3.1.1 Preliminary Results
77(3)
3.1.2 Inequalities Involving Ratios of Generalized Bessel Functions
80(2)
3.1.3 Inequalities Involving Ratios of Hypergeometric Functions
82(1)
3.1.4 Inequalities Involving Ratios of General Power Series
83(2)
3.2 Functional Inequalities Involving Special Functions
85(14)
3.2.1 Inequalities Involving Gaussian Hypergeometric Functions
85(6)
3.2.2 Inequalities Involving Generalized Bessei Functions
91(2)
3.2.3 Inequalities Involving Confluent Hypergeometric Functions
93(1)
3.2.4 Inequalities Involving General Power Series and Concluding Remarks
94(5)
3.3 Landen-Type Inequality for Bessei Functions
99(4)
3.3.1 Landen-Type Inequality for Generalized Bessei Functions
100(2)
3.3.2 Landen-Type Inequality for General Power Series
102(1)
3.4 Convexity of Hypergeometric Functions with Respect to Holder Means
103(9)
3.4.1 Introduction and Preliminaries
103(1)
3.4.2 Convexity of Hypergeometric Functions with Respect to Holder Means
104(4)
3.4.3 Convexity of General Power Series with Respect to Holder Means
108(2)
3.4.4 Concluding Remarks
110(2)
3.5 Askey's and Griinbaum's Inequality for Generalized Bessel Functions
112(6)
3.5.1 Askey's and Griinbaum's Inequality for Generalized Bessel Functions
113(2)
3.5.2 Lower and Upper Bounds for Generalized Bessel Functions
115(3)
3.6 Inequalities Involving Modified Bessei Functions
118(10)
3.7 Miscellaneous Inequalities Involving the Generalized Bessel Functions
128(33)
3.7.1 Mitrinovic's Inequality and Mahajan's Inequality
129(3)
3.7.2 Redheffer's Inequality
132(3)
3.7.3 Cusa's Inequality and Related Inequalities
135(4)
3.7.4 Extensions of Jordan's Inequality
139(5)
3.7.5 Sharp Jordan Type Inequalities for Bessel Functions
144(15)
3.7.6 The Sine and Hyperbolic Sine Integral
159(2)
3.8 Redheffer Type Inequalities for Bessel Functions
161(26)
3.8.1 An Extension of Redheffer's Inequality and Its Hyperbolic Analogue
162(3)
3.8.2 Sharp Exponential Redheffer-Type Inequalities for Bessel Functions
165(18)
3.8.3 A Lower Bound for the Gamma Function
183(4)
Appendix A
187(6)
A.1 Conjectures
187(1)
A.2 Open Problems
187(1)
A.3 Matlab Programs for Graphs
188(5)
References 193(10)
Index 203
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