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Special Functions and Orthogonal Polynomials (Hardcover, 2 Rev Ed)
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Special Functions and Orthogonal Polynomials (Hardcover, 2 Rev Ed)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 19 working days
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The subject of special functions is often presented as a collection
of disparate results, rarely organized in a coherent way. This book
emphasizes general principles that unify and demarcate the subjects
of study. The authors' main goals are to provide clear motivation,
efficient proofs, and original references for all of the principal
results. The book covers standard material, but also much more. It
shows how much of the subject can be traced back to two equations -
the hypergeometric equation and confluent hypergeometric equation -
and it details the ways in which these equations are canonical and
special. There is extended coverage of orthogonal polynomials,
including connections to approximation theory, continued fractions,
and the moment problem, as well as an introduction to new
asymptotic methods. There are also chapters on Meijer G-functions
and elliptic functions. The final chapter introduces Painleve
transcendents, which have been termed the 'special functions of the
twenty-first century'.
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