Integral Representations and Zeros of the Lommel Function and the Hypergeometric $$_1F_2$$ Function

IF 1.1 3区 数学 Q1 MATHEMATICS
Federico Zullo
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引用次数: 0

Abstract

We give different integral representations of the Lommel function \(s_{\mu ,\nu }(z)\) involving trigonometric and hypergeometric \(_2F_1\) functions. By using classical results of Pólya, we give the distribution of the zeros of \(s_{\mu ,\nu }(z)\) for certain regions in the plane \((\mu ,\nu )\). Further, thanks to a well known relation between the functions \(s_{\mu ,\nu }(z)\) and the hypergeometric \( _1F_2\) function, we describe the distribution of the zeros of \(_1F_2\) for specific values of its parameters.

Abstract Image

洛梅尔函数和超几何 $$1F_2$ 函数的积分表示和零点
我们给出了洛梅尔函数 \(s_{\mu ,\nu }(z)\的不同积分表示,涉及三角函数和超几何 \(_2F_1\)函数。通过使用 Pólya 的经典结果,我们给出了平面 \((\mu ,\nu )\) 中某些区域的 \(s_{\mu ,\nu }(z)\) 的零点分布。此外,由于函数 \(s_{\mu ,\nu }(z)\) 和超几何 \( _1F_2\)函数之间的关系众所周知,我们描述了 \(_1F_2\) 在其参数的特定值下的零点分布。
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来源期刊
Results in Mathematics
Results in Mathematics 数学-数学
CiteScore
1.90
自引率
4.50%
发文量
198
审稿时长
6-12 weeks
期刊介绍: Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.
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