Introduction to special functions
This is the first introductionary part of the course of special functions of hypergeometric type. We start from the survey of properties of Euler Gamma function, Riemann zeta function, Gauss hypergeometric function and its various degenerations - Whittaker, Bessel, Airy, Legendre functions etc., and their applications in mathematical physics.
The second part, which will take place in April-May, is devoted to further generalizations of classical hypergeometric functions – Barnes multiple Gamma function, double sine function, elliptic Gamma function, related hypergeometric integrals and their applications to integrable systems.
The second part, which will take place in April-May, is devoted to further generalizations of classical hypergeometric functions – Barnes multiple Gamma function, double sine function, elliptic Gamma function, related hypergeometric integrals and their applications to integrable systems.
Lecturer
Date
12th September ~ 31st October, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Thursday | 09:50 - 11:25 | A3-2a-302 | ZOOM 04 | 482 240 1589 | BIMSA |
Prerequisite
Basic calculus, Complex analysis and Ordinary differential equations
Syllabus
Part I: Classical hypergeometric functions
1. Euler Gamma function.
2. Riemann zeta function.
3. Gauss hypergeometric function.
4. Confluent hypergeometric functions. Bessel and Whitakker functions.
5. Special functions in representation theory and in mathematical physics
1. Euler Gamma function.
2. Riemann zeta function.
3. Gauss hypergeometric function.
4. Confluent hypergeometric functions. Bessel and Whitakker functions.
5. Special functions in representation theory and in mathematical physics
Reference
1. Whittaker, E. T., and G. N. Watson. "A Course of Modern Analysis, I, II. University press, 1920
2. Andrews, George E., et al. Special functions. Vol. 71. Cambridge: Cambridge university press, 1999.
3. LJ Slater. Generalized hyper geometric functions. London, Cambridge Univ. Press, 1966
4. Edwards, Harold M. Riemann's zeta function. Vol. 58. Courier Corporation, 2001.
5. Gasper, George, and Mizan Rahman. Basic hypergeometric series. Vol. 96. Cambridge university press, 2011.
6.Vilenkin N. I. A. Special functions and the theory of group representations. – American Mathematical Soc., 1978. – Т. 22.
2. Andrews, George E., et al. Special functions. Vol. 71. Cambridge: Cambridge university press, 1999.
3. LJ Slater. Generalized hyper geometric functions. London, Cambridge Univ. Press, 1966
4. Edwards, Harold M. Riemann's zeta function. Vol. 58. Courier Corporation, 2001.
5. Gasper, George, and Mizan Rahman. Basic hypergeometric series. Vol. 96. Cambridge university press, 2011.
6.Vilenkin N. I. A. Special functions and the theory of group representations. – American Mathematical Soc., 1978. – Т. 22.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Sergey Khoroshkin is a professor of Higher School of Economy in Moscow. His research interests include representation theory, quantum integrable systems and special functions.