DOI: 10.1002/mma.9939 ISSN: 0170-4214
Summing Sneddon–Bessel series explicitly
Antonio J. Durán, Mario Pérez, Juan Luis Varona We sum in a closed form the Sneddon–Bessel series
where
is an integer,
with
and
are the zeros of the Bessel function
of order
. In most cases, the explicit expressions for these sums involve hypergeometric functions
. As an application, we prove some extensions of the Kneser–Sommerfeld expansion. For instance, we show that
if
and
(here,
denotes the Bessel function of the second kind), which becomes the Kneser–Sommerfeld expansion when
.