Uniform upper bounds and the asymptotic expansion with an explicit remainder
term are established for the Macdonald function Kiτ​(x). The results can
be applied, for instance, to study the summability of the divergent
Kontorovich-Lebedev integrals in the sense of Jones. Namely, we answer
affirmatively a question (cf. [6]) whether these integrals converge for even
entire functions of the exponential type in a weak sense