## General Multi-sum Transformations and Some Implications. (arXiv:1901.01988v1 [math.NT])

We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence \$\{g(k)\}\$), to be reduced to an infinite \$q\$-product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some \$q\$ orthogonal polynomials, and various multi-sums that are expressible as infinite products.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence \$\{g(k)\}\$), to be reduced to an infinite \$q\$-product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some \$q\$ orthogonal polynomials, and various multi-sums that are expressible as infinite products.