Tian-Xiao He - Böcker

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding.Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical integration, partial differential equations and Green's functions, harmonic analysis, numerical analysis and approximation theory. In this work the exposition focuses primarily on a powerful tool which has become especially important in our computerized age, namely, dimensionality reducing expansion (DRE). The method of dimensionally reducing expansion (DRE) is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. Key features of this monograph include: fine exposition covering the history of the subject; up-to-date new results; presentation of dimensionality reducing expansion (DRE) technique using broad array of examples, illustrations and problem sets; balance between theory and applications; coverage of such related topics as boundary type quadratures and asymptotic expansions of oscillatory integrals; bibliography and index; and broad appeal to mathematicians, statisticians and physicists.

This volume contains papers selected from the Wavelet Analysis and Multiresolution Methods Session of the AMS meeting held at the University of Illinois at Urbana-Champaign. The contributions cover: construction, analysis, computation and application of multiwavelets; scaling vectors; nonhomogenous refinement; mulivariate orthogonal and biorthogonal wavelets; and other related topics.

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding.Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

This volume contains papers selected from the Wavelet Analysis and Multiresolution Methods Session of the AMS meeting held at the University of Illinois at Urbana-Champaign. The contributions cover: construction, analysis, computation and application of multiwavelets; scaling vectors; nonhomogenous refinement; mulivariate orthogonal and biorthogonal wavelets; and other related topics.

Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical analysis, approximation theory, partial differential equations, integral equations, harmonic analysis, etc. In this work the exposition focuses primarily on a powerful tool that has become especially important in our computerized age, namely, dimensionality reducing expansion (DRE). The method of DRE is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. To date, there is no comprehensive treatment of this subject in monograph or textbook form. Key features of this self-contained monograph include: * fine exposition covering the history of the subject * up-to-date new results, related to many fields of current research such as boundary element methods for solving PDEs and wavelet analysis * presentation of DRE techniques using a broad array of examples * good balance between theory and application * coverage of such related topics as boundary type quadratures and asymptotic expansions of oscillatory integrals * excellent and comprehensive bibliography and index This work will appeal to a broad audience of students and researchers in pure and applied mathematics, statistics, and physics, and can be used in a graduate/advanced undergraduate course or as a standard reference text.

The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field.