偏钟多项式与(q)的联系问)k;配分函数，以及某些q-超几何级数

JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2022-12-30 DOI:10.56827/jrsmms.2022.1001.1

Mushtaque Ahmed Pathan, J. Bulnes, J. L´opez-Bonilla, H. Kumar

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引用次数: 1

摘要

我们展示了q平移阶乘(q;q)n，以及不完全指数贝尔多项式，并使用Petkovsek-WilfZeilberger算法的q版来评估几个q-超几何级数。最后，我们将配分函数p(n)写成Qm(k)的形式，即使用不超过k的部分(可能是重复的)对m进行分区的次数。

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CONNECTION BETWEEN PARTIAL BELL POLYNOMIALS AND (q; q)k; PARTITION FUNCTION, AND CERTAIN q-HYPERGEOMETRIC SERIES

We exhibit a relationship between q-shifted factorial, (q; q)n, and the incomplete exponential Bell polynomials and also evaluate several q-hypergeometric series using the q-version of Petkovsek-WilfZeilberger’s algorithm. Finally, we write the partition function p(n) in terms of Qm(k), the number of partitions of m using (possibly repeated) parts that do not exceed k.

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JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES

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