  As well known, the study of Riemanns zeta function {\zeta}(s) involves the
related entire function {\xi}(s). A close relative of {\zeta}(s) is the
alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has
a corresponding entire function {\xi}_a (s). After establishing its definition
and a related functional equation, formulas based on incomplete gamma functions
are worked out, allowing to numerically evaluate {\xi}_a (s). Examples
verifying the obtained formulas are included.
