Special Functions and Orthogonal Polynomials (Cambridge by Richard Beals,Roderick Wong PDF

By Richard Beals,Roderick Wong

the topic of designated capabilities is frequently awarded as a set of disparate effects, infrequently equipped in a coherent means. This ebook emphasizes normal ideas that unify and demarcate the topics of analysis. The authors' major pursuits are to supply transparent motivation, effective proofs, and unique references for the entire primary effects. The e-book covers common fabric, but in addition even more. It exhibits how a lot of the topic will be traced again to 2 equations - the hypergeometric equation and confluent hypergeometric equation - and it information the ways that those equations are canonical and specified. there's prolonged assurance of orthogonal polynomials, together with connections to approximation idea, persisted fractions, and the instant challenge, in addition to an creation to new asymptotic tools. There also are chapters on Meijer G-functions and elliptic features. the ultimate bankruptcy introduces Painlevé transcendents, that have been termed the 'special capabilities of the twenty-first century'.

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Special Functions and Orthogonal Polynomials (Cambridge Studies in Advanced Mathematics) by Richard Beals,Roderick Wong

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