Special Functions and Their Symmetries: Postgraduate Course in Applied Analysis
by Vadim Kuznetsov, Vladimir Kisil
Publisher: University of Leeds 2003
This text presents fundamentals of special functions theory and its applications in partial differential equations of mathematical physics. The course covers topics in harmonic, classical and functional analysis, and combinatorics. It consists of the two parts: the first part gives the classic analytical approach and the second links the theory with groups of symmetries.
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In semi-classical analysis many of the basic results involve asymptotic expansions in which the terms can by computed by symbolic techniques and the focus of these lecture notes will be the 'symbol calculus' that this creates.
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