摘要
Gould-Hsu曾经发表了一类对于构造插值公式具有重要应用的互反关系,本文将建立其自然q-模拟。这时q-互反关系在下述意义下异于Carlitz的工作:当取q→1的极限时,本文提供的q-互反公式自动退化为著名的Gould-Hsu反演。当特殊指定两组自由参量时,本文的互反关系将产生一系列简洁的q-互反公式。作为应用,文中讨论了某些例证和卷积型恒等式。
Gould and Hsu [1] published a class of inverse relations, which have important applications in constructing interpolation formulas (of. [3-5]).Here we present their natural q-analogs which are different from those given by Carlitz[2], in the sense that when taking the limit of q→1 in the q-inverse relations our results automatically reduce to the original ones. For the particular choices of two sets of free parameters these inversions yield a series of explicit q-inverse relations. As applications, some instances and convolution-tyle identities are discussed.
出处
《应用数学》
CSCD
北大核心
1989年第1期47-52,共6页
Mathematica Applicata
