內容大鋼
The idea of preparing this volume was inspired by the invited lectures atthe "International Conference on Orthogonal Polynomials and q-Series",held at the University of Central Florida in Orlando, on May 10–12,2015. The conference was dedicated to Professor Mourad Ismail on his70th birthday. It was strongly felt that it would be useful and timelyto prepare an edited book highlighting important directions of researchon orthogonal polynomials, q-series, and related topics in approximationtheory, number theory, combinatorics, applied and computational harmonicanalysis. Ms. Rochelle Kronzek, Executive Editor of World Scientific, whoattended the conference, encouraged the idea, which ultimately led to apublishing agreement.
This volume contains 27 chapters exploring various topics on the frontierof research on orthogonal polynomials, q-series, and related topics men-tioned above. We strived for a book that would inspire young researchersand provide pleasant readings for the other generations of researchers inthese fields.
目錄
1.Mourad Ismail
2.Binomial Andrews–Gordon–Bressoud Identities
3.Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series
4.A Sturm–Liouville Theory for Hahn Difference Operator
5.Solvability of the Hankel Determinant Problem for Real Sequences
6.Convolution and Product Theorems for the Special Affine Fourier Transform
7.A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials
8.The Orthogonality of Al-Salam-Carlitz Polynomialsfor Complex Parameters
9.Crouching AGM, Hidden Modularity
10.Asymptotics of Orthogonal Polynomials and the Painlev? Transcendents
11.From the Gaussian Circle Problem to Multivariate Shannon Sampling
12.Weighted Partition Identities and Divisor Sums
13.On the Ismail-Letessier-Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials
14.A Discrete Top-Down Markov Problem in Approximation Theory
15.Supersymmetry of the Quantum Rotor
16.The Method of Brackets in Experimental Mathematics
17.Balanced Modular Parameterizations
18.Some Smallest Parts Functions from Variations of Bailey's Lemma
19.Dual Addition Formulas Associated with Dual Product Formulas
20.Holonomic Tools for Basic Hypergeometric Functions
21.A Direct Evaluation of an Integral of Ismail and Valent
22.Algebraic Generating Functions for Gegenbauer Polynomials
23.q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey
24.Summation Formulas for Noncommutative Hypergeometric Series
25.Asymptotics of Generalized Hypergeometric Functions
26.Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series
27.Certain Positive Semidefinite Matrices of Special Functions
編輯手記
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