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Analytic Number Theory, Approximation Theory, and Special Functions

In Honor of Hari M. Srivastava

  • Book
  • © 2014

Overview

Editors:
  1. Gradimir V. Milovanović

    1. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

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  2. Michael Th. Rassias

    1. Department of Mathematics, ETH Zürich, Zürich, Switzerland

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    You can also search for this editor in PubMed   Google Scholar

  • Presents mathematical results and open problems in a simple and self-contained manner

  • Contains new results in rapidly progressing areas of research in mathematics, engineering, cryptography, mathematical physics and economics

  • Provides a historical overview of analytic number theory, approximation theory and special functions

  • Includes supplementary material: sn.pub/extras

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xi
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  2. Analytic Number Theory, Combinatorics, and Special Sequences of Numbers and Polynomials

    1. Front Matter

      Pages 1-1
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    2. The Mean Values of the Riemann Zeta-Function on the Critical Line

      • Aleksandar Ivić
      Pages 3-68

    3. Explicit Bounds Concerning Non-trivial Zeros of the Riemann Zeta Function

      • Mehdi Hassani
      Pages 69-77

    4. On the Value-Distribution of Logarithmic Derivatives of Dirichlet L-Functions

      • Yasutaka Ihara, Kohji Matsumoto
      Pages 79-91

    5. Multiple Gamma Functions and Their Applications

      • Junesang Choi
      Pages 93-129

    6. On Partition Functions of Hyperbolic Three-Geometry and Associated Hilbert Schemes

      • A. A. Bytsenko, E. Elizalde
      Pages 131-148

    7. Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications

      • Yilmaz Simsek
      Pages 149-214

    8. Combinatorial Interpretation of a Generalized Basic Series

      • A. K. Agarwal, M. Rana
      Pages 215-225

    9. Identities for Reciprocal Binomials

      • Anthony Sofo
      Pages 227-238

    10. A Note on q-Stirling Numbers

      • Mircea Merca
      Pages 239-244

  3. Analytic Inequalities and Applications

    1. Front Matter

      Pages 245-245
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    2. A Survey on Cauchy–Bunyakovsky–Schwarz Inequality for Power Series

      • Alawiah Ibrahim, Silvestru Sever Dragomir
      Pages 247-295

    3. Topics in Special Functions III

      • Glen D. Anderson, Matti Vuorinen, Xiaohui Zhang
      Pages 297-345

    4. Completely Monotone Functions: A Digest

      • Milan Merkle
      Pages 347-364

    5. New Applications of Superquadracity

      • Shoshana Abramovich
      Pages 365-395

    6. Green’s Operator and Differential Forms

      • Shusen Ding, Yuming Xing
      Pages 397-427

    7. Multidimensional Discrete Hilbert-Type Inequalities, Operators and Compositions

      • Bicheng Yang
      Pages 429-484

    8. The Function (b x − a x)∕x: Ratio’s Properties

      • Feng Qi, Qiu-Ming Luo, Bai-Ni Guo
      Pages 485-494

    9. On the Approximation and Bounds of the Gini Mean Difference

      • Pietro Cerone
      Pages 495-516
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Keywords

About this book

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions.

The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Editors and Affiliations

  • Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  • Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

Bibliographic Information

  • Book Title: Analytic Number Theory, Approximation Theory, and Special Functions

  • Book Subtitle: In Honor of Hari M. Srivastava

  • Editors: Gradimir V. Milovanović, Michael Th. Rassias

  • DOI: https://doi.org/10.1007/978-1-4939-0258-3

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2014

  • Hardcover ISBN: 978-1-4939-0257-6Published: 04 March 2014

  • Softcover ISBN: 978-1-4939-4538-2Published: 03 September 2016

  • eBook ISBN: 978-1-4939-0258-3Published: 08 July 2014

  • Edition Number: 1

  • Number of Pages: XI, 880

  • Number of Illustrations: 24 illustrations in colour

  • Topics: Number Theory, Approximations and Expansions, Functional Analysis, Difference and Functional Equations

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