The purpose of this article is to study convergence regions and q-integral representations of certain non-symmetric q-Lauricella functions and quadruple functions in the spirit of Exton. In the process, we slightly improve Exton’s original formulas, notation, and convergence regions. There are three so-called q-real numbers, which are briefly introduced. These numbers occur both in the q-integrals and in the convergence regions. When q-integral expressions for the symmetric \({\Phi _{A }^{(n)}}\) and \({\Phi _{D }^{(n)}}\) are used in the proofs, in the first case, third q-real numbers occur in the q-integrals. When \({\Phi _{D }^{(n)}}\) is used in the proofs, the formulas are simpler, because the latter function has greater convergence region. Similarly, multiple q-Horn functions are briefly discussed.

本文的目的是本着 Exton 的精神，研究某些非对称q -Lauricella 函数和四元函数的收敛域和q积分表示。在此过程中，我们稍微改进了 Exton 的原始公式、符号和收敛区域。所谓q实数共有三个，简单介绍一下。这些数字同时出现在q积分和收敛区域中。当证明中使用对称\({\Phi _{A }^{(n)}}\)和\({\Phi _{D }^{(n)}}\) 的q积分表达式时，在第一种情况下，第三个q - 实数出现在q中-积分。当证明中使用\({\Phi _{D }^{(n)}}\)时，公式更简单，因为后者的收敛区域更大。类似地，简要讨论了多个q -Horn 功能。