论文标题
Ramanujan的主定理的操作计算概括
An Operational Calculus Generalization of Ramanujan's Master Theorem
论文作者
论文摘要
我们使用操作方法对Ramanujan的主定理进行正式扩展。所得的身份将积分在半线上的乘积计算转换为拉普拉斯变换的计算。由于身份纯粹是正式的，因此我们显示了这种操作方法的一致性以及各种标准的演算结果，然后进行了几个示例，以说明扩展的力量。然后，我们简要讨论了Ramanujan的主定理与Hardy和Carr的身份之间的联系，然后以我们扩展Ramanujan的方式扩展了后者的身份。最后，我们将结果概括，从而产生其他有趣的身份作为推论。
We give a formal extension of Ramanujan's master theorem using operational methods. The resulting identity transforms the computation of a product of integrals on the half-line to the computation of a Laplace transform. Since the identity is purely formal, we show consistency of this operational approach with various standard calculus results, followed by several examples to illustrate the power of the extension. We then briefly discuss the connection between Ramanujan's master theorem and identities of Hardy and Carr before extending the latter identities in the same way we extended Ramanujan's. Finally, we generalize our results, producing additional interesting identities as a corollary.
