论文标题
与某些Q-Mellin-Barnes积分相关的非终止转换和求和
Nonterminating transformations and summations associated with some q-Mellin--Barnes integrals
论文作者
论文摘要
在许多情况下，人们可能会遇到$ Q $ -Mellin--Barnes类型的积分。这些积分很容易地使用具有悠久历史的定理来评估，其历史可以追溯到Slater，Askey，Gasper，Rahman等。我们得出了一些有趣的$ Q $ -Mellin--Barnes积分，并使用它们得出了转换和求和公式，以实现非终止基本高几何函数。 The cases which we treat include ratios of theta functions, the Askey--Wilson moments, nonterminating well-poised ${}_3ϕ_2$, nonterminating very-well-poised ${}_5W_4$, ${}_8W_7$, products of two nonterminating ${}_2ϕ_1$'s, square of a nonterminating well-poised $ {} _ 2ϕ_1 $，而非终止$ {} _ {12} w_ {11} $和$ {} _ {10} w_9 $。
In many cases one may encounter an integral which is of $q$-Mellin--Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interesting $q$-Mellin--Barnes integrals and using them we derive transformation and summation formulas for nonterminating basic hypergeometric functions. The cases which we treat include ratios of theta functions, the Askey--Wilson moments, nonterminating well-poised ${}_3ϕ_2$, nonterminating very-well-poised ${}_5W_4$, ${}_8W_7$, products of two nonterminating ${}_2ϕ_1$'s, square of a nonterminating well-poised ${}_2ϕ_1$, and nonterminating ${}_{12}W_{11}$ and ${}_{10}W_9$.
