Contiguity relations for $q$-hypergeometric function and related quantum group
نویسندگان
چکیده
منابع مشابه
A Connection Formula for the q-Confluent Hypergeometric Function
We show a connection formula for the q-confluent hypergeometric functions 2φ1(a, b; 0; q, x). Combining our connection formula with Zhang’s connection formula for 2φ0(a, b;−; q, x), we obtain the connection formula for the q-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer’s confluent hypergeometric functions by taking the limit q → 1− of our...
متن کاملQuantum alpha-determinants and q-deformed hypergeometric polynomials
The quantum α-determinant is defined as a parametric deformation of the quantum determinant. We investigate the cyclic Uq(sl2)-submodules of the quantum matrix algebra Aq(Mat2) generated by the powers of the quantum α-determinant. For such a cyclic module, there exists a collection of polynomials which describe the irreducible decomposition of it in the following manner: (i) each polynomial cor...
متن کاملHypergeometric functions related to Schur Q-polynomials and BKP equation
We introduce hypergeometric functions related to projective Schur functions Qλ and describe their properties. Linear equations, integral representations and Pfaffian representations are obtained. These hypergeometric functions are vacuum expectations of free fermion fields, and thus these functions are tau functions of the so-called BKP hierarchy of integrable equations. 1 Hypergeometric series...
متن کاملThe Q-twisted Cohomology and the Q-hypergeometric Function at |q| = 1
We construct the q-twisted cohomology associated with the q-multiplicative function of Jordan-Pochhammer type at |q| = 1. In this framework, we prove the Heine’s relations and a connection formula for the q-hypergeometric function of the Barnes type. We also prove an orthogonality relation of the q-little Jacobi polynomials at |q| = 1.
متن کاملBilinear generating relations for a family of q-polynomials and generalized basic hypergeometric functions
In this paper, we derive a bilinear q-generating function involving basic analogue of Fox’s H-function and a general class of q-hypergeometric polynomials. Applications of the main results are also illustrated.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1992
ISSN: 0386-2194
DOI: 10.3792/pjaa.68.157