کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665853 1633836 2014 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation
چکیده انگلیسی

This paper is devoted to the family {Gn}{Gn} of hypergeometric series of any finite number of variables, the coefficients being the square of the multinomial coefficients (ℓ1+⋯+ℓn)!/(ℓ1!…ℓn!)(ℓ1+⋯+ℓn)!/(ℓ1!…ℓn!), where n∈Z⩾1n∈Z⩾1. All these series belong to the family of the general Appell–Lauricellaʼs series. It is shown that each function GnGn can be expressed by an integral involving the previous one, Gn−1Gn−1. Thus this family can be represented by a multidimensional Euler type integral, what suggests some explicit link with the Gelfand–Kapranov–Zelevinskyʼs theory of A  -hypergeometric systems or with the Aomotoʼs theory of hypergeometric functions. The quasi-invariance of each function GnGn with regard to the action of a finite number of involutions of C⁎nC⁎n is also established. Finally, a particular attention is reserved to the study of the functions G2G2 and G3G3, each of which is proved to be algebraic or to be expressed by the Legendreʼs elliptic function of the first kind.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 252, 15 February 2014, Pages 652–683
نویسندگان
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