论文标题
Lobachevsky型公式通过傅立叶分析
Lobachevsky-type Formulas via Fourier Analysis
论文作者
论文摘要
最近，人们对洛巴乔夫斯基型积分的兴趣和涉及基本正弦的有趣身份激励了经典的parseval公式的扩展，涉及周期性和非周期性功能。我们开发了Parseval公式的版本，该版本在应用程序中通常更实用，并通过扩展了对Lobachevsky型积分的最新结果来说明其使用。一些以前已知的有趣的身份以更透明的方式重新传播，并给出了涉及基本正弦和贝塞尔功能的积分的新公式。
Recently renewed interest in the Lobachevsky-type integrals and interesting identities involving the cardinal sine motivate an extension of the classical Parseval formula involving both periodic and non-periodic functions. We develop a version of the Parseval formula that is often more practical in applications and illustrate its use by extending recent results on Lobachevsky-type integrals. Some previously known, interesting identities are re-proved in a more transparent manner and new formulas for integrals involving cardinal sine and Bessel functions are given.
