اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدElliptic hypergeometric functions
396
0
0.0
(
0
)
تأليف
V.P. Spiridonov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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 som
e of its properties are described. Present review is based on authors habilitation thesis [Spi7] containing a more detailed account of the subject.
Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the argument
variable. The paper presents general elementary expressions of these dihedral hypergeometric functions, involving finite bivariate sums expressible as terminating Appells F2 or F3 series. Additionally, trigonometric expressions for the dihedral functions are presented, and degenerate cases (logarithmic, or with the monodromy group Z/2Z) are considered.
We give a brief account of the key properties of elliptic hypergeometric integrals -- a relatively recently discovered top class of transcendental special functions of hypergeometric type. In particular, we describe an elliptic generalization of Eule
rs and Selbergs beta integrals, elliptic analogue of the Euler-Gauss hypergeometric function and some multivariable elliptic hypergeometric functions on root systems. The elliptic Fourier transformation and corresponding integral Bailey lemma technique is outlined together with a connection to the star-triangle relation and Coxeter relations for a permutation group. We review also the interpretation of elliptic hypergeometric integrals as superconformal indices of four dimensional supersymmetric quantum field theories and corresponding applications to Seiberg type dualities.
The aim of this work is to demonstrate various an interesting recursion formulas, differential and integral operators, integration formulas, and infinite summation for each of Horns hypergeometric functions $mathrm{H}_{1}$, $mathrm{H}_{2}$, $mathrm{H
}_{3}$, $mathrm{H}_{4}$, $mathrm{H}_{5}$, $mathrm{H}_{6}$ and $mathrm{H}_{7}$ by the contiguous relations of Horns hypergeometric series. Some interesting different cases of our main consequences are additionally constructed.
We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painleve equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The soluti
ons are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridonovs elliptic beta integral.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
