01865nmm a2200265 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001200139100002200151245007500173260004800248300002700296653002700323653004000350700002300390041001900413989003200432490005300464856006300517082001100580520100800591EB001382777EBX0100000000000000090574200000000000000.0cr|||||||||||||||||||||170324 ||| eng a9780511565717 4aQA404.51 aDunkl, Charles F.00aOrthogonal polynomials of several variablescCharles F. Dunkl, Yuan Xu aCambridgebCambridge University Pressc2001 axv, 390 pagesbdigital aOrthogonal polynomials aFunctions of several real variables1 aXu, Yuane[author]07aeng2ISO 639-2 bCBOaCambridge Books Online0 aEncyclopedia of mathematics and its applications uhttps://doi.org/10.1017/CBO9780511565717xVerlag3Volltext0 a515.55 aThis is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate analysis, including approximations and numerical integration. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball, or those of Gaussian type, for which fairly explicit formulae exist. The approach is a blend of classical analysis and symmetry-group-theoretic methods. Reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers