This paper presents closed-form expressions for the series,
, where the sum is from
n = 1 to
n = ∞. These expressions were obtained by recasting the series in a different form, followed by the use of certain relationships involving the elliptical nome. Among the values of
x for which these expressions can be obtained are of the form:
and
, where l is an integer between
–∞ and ∞. The values of
λ include 1,
,
and 3. Examples of closed-form expressions obtained in this manner are first presented for
,
,
, and
. Additional examples are then presented for
,
,
, and
. This undertaking was prompted by the author’s work on an electrostatics boundary-value problem related to the van der Pauw measurement technique of electrical resistivity. The presence of this series for
x =
in the solution of that problem and its absence from any compendium of infinite series that he consulted led to this work.