A procedure for generating infinite series identities
نویسنده
چکیده
A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation. Identities are generated involving both elementary and special functions. Infinite sums of special functions include those of the gamma and polygamma functions, the Hurwitz Zeta function, the polygamma function, the Gauss hypergeometric function, and the Lerch transcendent. The procedure can be automated with Mathematica (or equivalent software).
منابع مشابه
Overpartitions and Generating Functions for Generalized Frobenius Partitions
Generalized Frobenius partitions, or F -partitions, have recently played an important role in several combinatorial investigations of basic hypergeometric series identities. The goal of this paper is to use the framework of these investigations to interpret families of infinite products as generating functions for F -partitions. We employ q-series identities and bijective combinatorics.
متن کاملDiscovering and Proving Infinite Binomial Sums Identities
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of π or log(2). In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals. Using substitutions, we express the inter...
متن کاملAn Extension to Overpartitions of the Rogers-ramanujan Identities for Even Moduli
We study a class of well-poised basic hypergeometric series J̃k,i(a;x; q), interpreting these series as generating functions for overpartitions defined by multiplicity conditions on the number of parts. We also show how to interpret the J̃k,i(a; 1; q) as generating functions for overpartitions whose successive ranks are bounded, for overpartitions that are invariant under a certain class of conju...
متن کاملGrowth in Varieties of Multioperator Algebras and Groebner Bases in Operads
We consider varieties of linear multioperator algebras, that is, classes of algebras with several multilinear operations satisfying certain identities. To each such a variety one can assign a numerical sequence called a sequence of codimensions. The n-th codimension is equal to the dimension of the vector space of all n-linear operations in the free algebra of the variety. In recent decades, a ...
متن کاملThe Dual of Göllnitz’s (big) Partition Theorem*
A Rogers-Ramanujan (R-R) type identity is a q-hypergeometric identity in the form of an infinite (possibly multiple) series equals an infinite product. The series is the generating function of partitions whose parts satisfy certain difference conditions, whereas the product is the generating function of partitions whose parts usually satisfy certain congruence conditions. For a discussion of a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004