ترغب بنشر مسار تعليمي؟ اضغط هنا

Classical elliptic hypergeometric functions and their applications

102   0   0.0 ( 0 )
 نشر من قبل Vyacheslav P. Spiridonov
 تاريخ النشر 2005
  مجال البحث فيزياء
والبحث باللغة English
 تأليف V.P. Spiridonov




اسأل ChatGPT حول البحث

General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the classical special functions. In particular, an elliptic analogue of the Gauss hypergeometric function and some of its properties are described. Present review is based on authors habilitation thesis [Spi7] containing a more detailed account of the subject.



قيم البحث

اقرأ أيضاً

402 - V.P. Spiridonov 2016
This is a brief overview of the status of the theory of elliptic hypergeometric functions to the end of 2012 written as a complementary chapter to the Russian edition of the book by G.E. Andrews, R. Askey, and R. Roy, Special Functions, Encycl. of Math. Appl. 71, Cambridge Univ. Press, 1999.
The Cholesky factorization of the moment matrix is applied to discrete orthogonal polynomials on the homogeneous lattice. In particular, semiclassical discrete orthogonal polynomials, which are built in terms of a discrete Pearson equation, are studi ed. The Laguerre-Freud structure semi-infinite matrix that models the shifts by $pm 1$ in the independent variable of the set of orthogonal polynomials is introduced. In the semiclassical case it is proven that this Laguerre-Freud matrix is banded. From the well known fact that moments of the semiclassical weights are logarithmic derivatives of generalized hypergeometric functions, it is shown how the contiguous relations for these hypergeometric functions translate as symmetries for the corresponding moment matrix. It is found that the 3D Nijhoff-Capel discrete Toda lattice describes the corresponding contiguous shifts for the squared norms of the orthogonal polynomials. The continuous Toda for these semiclassical discrete orthogonal polynomials is discussed and the compatibility equations are derived. It also shown that the Kadomtesev-Petvishvilii equation is connected to an adequate deformed semiclassical discrete weight, but in this case the deformation do not satisfy a Pearson equation.
162 - Masatoshi Noumi 2015
We propose a class of Pade interpolation problems whose solutions are expressible in terms of determinants of hypergeometric series.
A special singular limit $omega_1/omega_2to 1$ is considered for the Faddeev modular quantum dilogarithm (hyperbolic gamma function) and corresponding hyperbolic integrals. It brings a new class of hypergeometric identities associated with bilateral sums of Mellin-Barnes type integrals of particular Pochhammer symbol products.
In cite{GUW} we introduced a class of semi-classical functions of isotropic type, starting with a model case and applying Fourier integral operators associated with canonical transformations. These functions are a substantial generalization of the os cillatory functions of Lagrangian type that have played major role in semi-classical and micro-local analysis. In this paper we exhibit more clearly the nature of these isotropic functions by obtaining oscillatory integral expressions for them. Then we use these to prove that the classes of isotropic functions are equivariant with respect to the action of general FIOs (under the usual clean-intersection hypothesis). The simplest examples of isotropic states are the coherent states, a class of oscillatory functions that has played a pivotal role in mathematics and theoretical physics beginning with their introduction by of Schrodinger in the 1920s. We prove that every oscillatory function of isotropic type can be expressed as a superposition of coherent states, and examine some implications of that fact. We also show that certain functions of elliptic operators have isotropic functions for Schwartz kernels. This lead us to a result on an eigenvalue counting function that appears to be new (Corollary ref{cor:altWeyl}).
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا