اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدShort proofs of the elliptic beta integrals
65
0
0.0
(
0
)
تأليف
V.P. Spiridonov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give elementary proofs of the univariate elliptic beta integral with bases $|q|, |p|<1$ and its multiparameter generalizations to integrals on the $A_n$ and $C_n$ root systems. We prove also some new unit circle multiple elliptic beta integrals, which are well defined for $|q|=1$, and their $pto 0$ degenerations.
قيم البحث
اقرأ أيضاً
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.
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
When introduced in a 2018 article in the American Mathematical Monthly, the omega integral was shown to be an extension of the Riemann integral. Although results for continuous functions such as the Fundamental Theorem of Calculus follow immediately,
a much more satisfying approach would be to provide direct proofs not relying on the Riemann integral. This note provides those proofs.
First some definite integrals of W. H. L. Russell, almost all with trigonometric function integrands, are derived, and many generalized. Then a list is given in Russell-style of generalizations of integral identities of Amdeberhan and Moll. We conclu
de with a brief and noncomprehensive description of directions for further investigation, including the significant generalization to elliptic functions.
We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue calculus. In the one variable case, we get theta funct
ion extensions of the Meijer function. A number of multiple generalizations of the elliptic beta integral [S2] associated with the root systems $A_n$ and $C_n$ is described. Some of the $C_n$-examples were proposed earlier by van Diejen and the author, but other integrals are new. An example of the biorthogonality relations associated with the elliptic beta integrals is considered in detail.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
