Analytic Number Theory, Approximation Theory, and Special Functions [recurso electrónico] In Honor of Hari M. Srivastava

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 The mean values of the Riemann Zeta-functions on the critical line / Aleksandar Ivić Explicit bounds concerning non-trival zeros of the Riemann Zeta function / Mehdi Hassani On the value-distribution of logarithmic derivatives of Dirichlet L-functions / Yasutaka Ihara and Kohji Matsumoto Multiple gamma functions and their applications / Junesang Choi On partition functions of hyperbolic three-geometry and associated Hilbert schemes / A.A. Bytsenko and E. Elizalde Families of twisted Bernoulli numbers, twisted Bernoulli polynomials, and their applications / Simsek Combinatorial interpretation of a generalized basic series / A.K. Agarwal and M. Rana Identities for reciprocal binomials / Anthony Sofo A note on q-Stirling numbers / Mircea Merca A survey on Cauchy-Bunyakovsky-Schwarz inequality for power series / Alawiah Ibrahim and Silvestru Sever Dragonmir Topics in special functions III / Glen D. Anderson, Matti Vuorinen and Xiaohui Zhang ^ Completely monotone functions: a digest / Milan Merkle New applications of superquadracity / Shoshana Abramovich Green's operator and differential forms / Shusen Ding and Yuming Xing Multidimensional discrete Hilbert-type inequalities, operators and compositions / Bicheng Yang The functions (b[superscript]x - a[superscript]x)/x: ratio's properties / Feng Qi, Qiu-Ming Luo and Bai-Ni Guo On the approximation and bounds of the Gini mean difference / Pietro Cerone On parametric nonconvex variational inequalities / Muhammad Aslam Noor Simultaneous approximation for Stancu-type generalization of certain summation-integral-type operators / N.K. Govil and Vijay Gupta Korovkin-type approximation theorem for functions of two variables via statistical summability (C,1,1) / M. Mursaleen and S.A. Mohiuddine Reflections on the Baker-Gammel-Wills (Padé) conjecture / Doron S. Lubinsky ^ Optimal quadrature formulas and interpolation splines minimizing the semi-norm in the Hilbert space K2(P2) / Abdullo R. Hayotov, Gradimir V. Milovaović and Kholmat M. Shadimetov Numerical integration of highly oscillating functions / Gradimir V. Milovanović and Marija P. Stanić Asymptotic reductions between the Wilson polynomials and the lower level polynomials of the Askey scheme / Chelo Ferreira, José L. López and Ester Pérez Sinusía On a direct Uvarov-Chihara problem and some extensions / K. Castillo L. Garza and F. Marcellán On especial cases of Boas-Buck-type polynominal sequences / Ana F. Loureiro and S. Yakubovich Goursat's hypergeometric transformations, revisited / Per W. Karlsson Convolution product and differential and integro: differential equations / Adem Kılıçman Orthogonally additive: additive functional equation / Choonkil Park ^ Alternating Mathieu series, Hilbert-Eisenstein series and their generalized omega functions / Árpád Baricz, Paul L. Butzer and Tibor K. Pogány Properties of the product of modified Bessel functions / Árpád Baricz and Tibor K. Pogány Mapping properties of an integral operator involving Bessel functions / Saurabh Porwal and Daniel Breaz Poincaré [alpha]-series for classical Schottky groups / Vladimir V. Mityushev Inclusion properties for certain classes of meromorphic multivalent functions / Nak Eun Cho A journey from Gross-problem to Fujimoto-condition / Indrajit Lahiri and Abhijit Banerjee. Front Matter....Pages i-xi Front Matter....Pages 1-1 The Mean Values of the Riemann Zeta-Function on the Critical Line....Pages 3-68 Explicit Bounds Concerning Non-trivial Zeros of the Riemann Zeta Function....Pages 69-77 On the Value-Distribution of Logarithmic Derivatives of Dirichlet L -Functions....Pages 79-91 Multiple Gamma Functions and Their Applications....Pages 93-129 On Partition Functions of Hyperbolic Three-Geometry and Associated Hilbert Schemes....Pages 131-148 Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications....Pages 149-214 Combinatorial Interpretation of a Generalized Basic Series....Pages 215-225 Identities for Reciprocal Binomials....Pages 227-238 A Note on q -Stirling Numbers....Pages 239-244 Front Matter....Pages 245-245 A Survey on Cauchy–Bunyakovsky–Schwarz Inequality for Power Series....Pages 247-295 Topics in Special Functions III....Pages 297-345 Completely Monotone Functions: A Digest....Pages 347-364 New Applications of Superquadracity....Pages 365-395 Green’s Operator and Differential Forms....Pages 397-427 Multidimensional Discrete Hilbert-Type Inequalities, Operators and Compositions....Pages 429-484 The Function ( b x − a x )∕ x : Ratio’s Properties....Pages 485-494 On the Approximation and Bounds of the Gini Mean Difference....Pages 495-516 On Parametric Nonconvex Variational Inequalities....Pages 517-527 Front Matter....Pages 529-529 Simultaneous Approximation for Stancu-Type Generalization of Certain Summation–Integral-Type Operators....Pages 531-548 Korovkin-Type Approximation Theorem for Functions of Two Variables Via Statistical Summability ( C , 1, 1)....Pages 549-560 Front Matter....Pages 529-529 Reflections on the Baker–Gammel–Wills (Padé) Conjecture....Pages 561-571 Optimal Quadrature Formulas and Interpolation Splines Minimizing the Semi-Norm in the Hilbert Space $$K_{2}(P_{2})$$ ....Pages 573-611 Numerical Integration of Highly Oscillating Functions....Pages 613-649 Front Matter....Pages 651-651 Asymptotic Reductions Between the Wilson Polynomials and the Lower Level Polynomials of the Askey Scheme....Pages 653-690 On a Direct Uvarov-Chihara Problem and Some Extensions....Pages 691-704 On Especial Cases of Boas-Buck-Type Polynomial Sequences....Pages 705-720 Goursat’s Hypergeometric Transformations, Revisited....Pages 721-736 Convolution Product and Differential and Integro: Differential Equations....Pages 737-758 Orthogonally Additive: Additive Functional Equation....Pages 759-772 Front Matter....Pages 773-773 Alternating Mathieu Series, Hilbert–Eisenstein Series and Their Generalized Omega Functions....Pages 775-808 Properties of the Product of Modified Bessel Functions....Pages 809-820 Mapping Properties of an Integral Operator Involving Bessel Functions....Pages 821-826 Poincaré $$\boldsymbol{\alpha }$$ -Series for Classical Schottky Groups....Pages 827-852 Inclusion Properties for Certain Classes of Meromorphic Multivalent Functions....Pages 853-863 A Journey from Gross-Problem to Fujimoto-Condition....Pages 865-877 Back Matter....Pages 879-880