正交多项式和q-级数的前沿(英文)
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作者(美)M.祖海尔·纳什德//李欣|责编:刘家琳//李烨
出版社哈尔滨工业大学
ISBN9787576703740
出版时间2022-09
装帧其他
开本其他
定价98元
货号31685856
上书时间2024-05-29
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目录
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 Painlevé 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
编辑手记
内容摘要
Theideaofpreparingthisvolumewasinspiredbytheinvitedlecturesatthe\"InternationalConferenceonOrthogonalPolynomialsandq-Series\",heldattheUniversityofCentralFloridainOrlando,onMay10–12,2015.TheconferencewasdedicatedtoProfessorMouradIsmailonhis70thbirthday.Itwasstronglyfeltthatitwouldbeusefulandtimelytoprepareaneditedbookhighlightingimportantdirectionsofresearchonorthogonalpolynomials,q-series,andrelatedtopicsinapproximationtheory,numbertheory,combinatorics,appliedandcomputationalharmonicanalysis.Ms.RochelleKronzek,ExecutiveEditorofWorldScientific,whoattendedtheconference,encouragedtheidea,whichultimatelyledtoapublishingagreement.Thisvolumecontains27chaptersexploringvarioustopicsonthefrontierofresearchonorthogonalpolynomials,q-series,andrelatedtopicsmen-tionedabove.Westrivedforabookthatwouldinspireyoungresearchersandprovidepleasantreadingsfortheothergenerationsofresearchersinthesefields.
精彩内容本书重点介绍了正交多项式、q-级数和近似理论、数论、组合学、应用和计算谐波分析中的相关主题。本书共包含了27章，具体内容包括：二项安德罗斯-戈登-布雷苏(Andrews-Gordon-Bressoud)恒等式、哈恩差分算子的施图姆刘维尔理论、汉克尔行列式问题的可解性、卷积与特殊仿射变换的乘积定理、正交多项式的渐进与潘勒韦(Painleve)超越函数、从高斯圆问题到多元香农(Shannon)抽样、加权分拆恒等式和除数和、量子旋度的超对称性、贝利(Bailey)引理变分中的最小部分函数等相关内容。
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