ABEL’S METHOD ON SUMMATION BY PARTS AND BALANCED q-SERIES IDENTITIES
نویسنده
چکیده
The Abel method on summation by parts is reformulated to present new and elementary proofs of several classical identities of terminating balanced basic hypergeometric series. The examples strengthen our conviction that as traditional analytical instrument, the revised Abel method on summation by parts is indeed a very natural choice for working with basic hypergeometric series.
منابع مشابه
Explicit Resilient Functions Matching Ajtai-Linial
A Boolean function on n variables is q-resilient if for any subset of at most q variables, the function is very likely to be determined by a uniformly random assignment to the remaining n − q variables; in other words, no coalition of at most q variables has significant influence on the function. Resilient functions have been extensively studied with a variety of applications in cryptography, d...
متن کاملSolving the Balance Problem of On-Line Role-Playing Games Using Evolutionary Algorithms
In on-line role-playing games (RPG), each race holds some attributes and skills. Each skill contains several abilities such as physical damage, hit rate, etc. Parts of the attributes and all the abilities are a function of the character’s level, which are called Ability-Increasing Functions (AIFs). A well-balanced on-line RPG is characterized by having a set of well-balanced AIFs. In this paper...
متن کاملOn a Balanced Property of Compositions
Let S be a finite set of positive integers with largest element m. Let us randomly select a composition a of the integer n with parts in S, and let m(a) be the multiplicity of m as a part of a. Let 0 ≤ r < q be integers, with q ≥ 2, and let pn,r be the probability that m(a) is congruent to r modulo q. We show that if S satisfies a certain simple condition, then limn→∞ pn,r = 1/q. In fact, we sh...
متن کاملBalanced Partitions
A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. We begin by establishing a less well-known companion result, which states that both of these quantities are equal to the number of partitions of n into even parts along with exactly one triangular part. We then introduce the characteristic of a partition, which is...
متن کاملA new formulation of WRFDA analysis control variables
Background error covariance matrix B plays a crucial role in data assimilation. It ensures a balance preserving transfer of observational information to the unobserved parts of a computational domain. Storage and manipulation require reduction of the number of its non-null entries. In general, reduction is ensured via an appropriate diagonalization procedure resulting in a necessity of storing ...
متن کامل