通过拉曼努强主定理论有限梅林变换

arXiv - MATH - General Mathematics Pub Date : 2024-09-10 DOI:arxiv-2409.06304

Omprakash Atale

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引用次数: 0

摘要

本文旨在说明，通过利用拉马努强的主定理和下不完全伽马函数的性质，可以为函数 $f(x)$ 构造一个有限梅林变换，该函数在 $x$ 的正积分幂中有无穷次展开。通过对某些定积分进行求值，讨论了一些应用。此外，还将得到的解与 Mathematica 的结果进行比较，以检验计算的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Finite Mellin Transform via Ramanujan's Master Theorem

This paper aims to show that by making use of Ramanujan's Master Theorem and the properties of the lower incomplete gamma function, it is possible to construct a finite Mellin transform for the function $f(x)$ that has infinite series expansions in positive integral powers of $x$. Some applications are discussed by evaluating certain definite integrals. The obtained solutions are also compared with results from Mathematica to test the validity of the calculations.

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arXiv - MATH - General Mathematics

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