Upon reading the famous book on integral transforms volume II by Erdeyli et al., we encounter a formula which we use to derive a Mellin transform given by , where the parameters , and are general complex numbers. This Mellin transform will be derived in terms of the Lerch function and is not listed in current literature to the best of our knowledge. We will use this transform to create a table of definite integrals which can be used to extend similar tables in current books featuring such formulae.

中文翻译：

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Lerch 函数对对数和有理商函数的梅林变换

在阅读 Erdeyli 等人的关于积分变换的著名著作第 II 卷时，我们遇到了一个公式，我们用它来推导梅林变换，由下式给出 ,其中参数，并且是一般复数。这个梅林变换将根据 Lerch 函数推导出来，据我们所知，目前的文献中没有列出。我们将使用此变换创建一个定积分表，该表可用于扩展当前具有此类公式的书籍中的类似表。