## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# The Sign of Lommel's Function

J. Steinig
Transactions of the American Mathematical Society
Vol. 163 (Jan., 1972), pp. 123-129
DOI: 10.2307/1995711
Stable URL: http://www.jstor.org/stable/1995711
Page Count: 7
Preview not available

## Abstract

Lommel's function $s_{\mu, v}(x)$ is a particular solution of the differential equation $x^2y'' + xy' + (x^2 - v^2)y = x^{\mu + 1}$. It is shown here that $s_{\mu, v}(x) > 0$ for $x > 0$, if $\mu = \frac{1}{2}$ and $|v| < \frac{1}{2}$, or if $\mu > \frac{1}{2}$ and $|v| \leqq \mu$. This includes earlier results of R. G. Cooke's. The sign of $s_{\mu, v}(x)$ for other values of $\mu$ and $v$ is also discussed.

• 123
• 124
• 125
• 126
• 127
• 128
• 129