caa a22 4500 475839625 CHVBK 20180406123858.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1006390032014 doi (NATIONALLICENCE)springer-10.1023/A:1006390032014 Kitaev A. Steklov Mathematical Institute, Fontanka 27, 191011, St. Petersburg, Russia. e-mail aut Special Functions of the Isomonodromy Type [Elektronische Daten] [A. Kitaev] We introduce a new notion, a special function of the isomonodromy type, and show that most of the functions known in applied mathematics and mathematical physics as special functions belong to this type. This definition provides a unified approach to the theories of ‘linear' special functions, i.e., classical higher transcendental functions, and ‘nonlinear' special functions, i.e., functions of the Painlevé type. We also show that our definition has not only a conceptual (methodological) value; many well-known properties of the single-variable special functions can be re-derived not only from the isomonodromy point of view, but also the practical one too: (1) the isomonodromy approach is already known as an extremely useful one in the theory of Painlevé functions, (2) many properties (some of them can be new ones) of the multi-variable special functions can be obtained on a regular basis, and (3) the definition gives rise to several interesting mathematical questions which are discussed in the paper. We also make some remarks concerning the analogous description (via q-deformations) of q-special functions. Kluwer Academic Publishers, 2000 isomonodromy deformations nationallicence linear ordinary differential equations nationallicence Painlevé transcendents nationallicence gamma and beta functions nationallicence Gauss hypergeometric function nationallicence Bessel function nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers 64/1(2000-10-01), 1-32 0167-8019 64:1<1 2000 64 10440 https://doi.org/10.1023/A:1006390032014 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006390032014 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kitaev A. Steklov Mathematical Institute, Fontanka 27, 191011, St. Petersburg, Russia. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 64/1(2000-10-01), 1-32 0167-8019 64:1<1 2000 64 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer