Incomplete Cylindrical Functions of Sonine-Schlaefli Form and the Incomplete Weber Integrals

Abstract

Up to this point we have considered the incomplete cylindrical functions starting from their most general integral representations in either Poisson form

$$ {z^v}\int\limits_a^b{{e^{izt}}{{\left({{t^2}-1}\right)}^{v-1/2}}dt} $$

(1.1)

or in Bessel form

$$ \int\limits_a^b {{e^{z\sinh t - vt}}dt} $$

(1.2)

.