  The Kepler K2 mission now makes it possible to find and study a wider variety
of eclipsing binary stars than has been possible to-date, particularly
long-period systems with narrow eclipses. Our aim is to characterise eclipsing
binary stars observed by the Kepler K2 mission with orbital periods longer than
$P\approx 5.5$ days. The $ellc$ binary star model has been used to determine
the geometry of eclipsing binary systems in Kepler K2 campaigns 1, 2 and 3. The
nature of the stars in each binary is estimated by comparison to stellar
evolution tracks in the effective temperature - mean stellar density plane. 43
eclipsing binary systems have been identified and 40 of these are characterised
in some detail. The majority of these systems are found to be late-type dwarf
and sub-giant stars with masses in the range 0.6 to 1.4 solar masses. We
identify two eclipsing binaries containing red giant stars, including one
bright system with total eclipses that is ideal for detailed follow-up
observations. The bright B3V-type star HD142883 is found to be an eclipsing
binary in a triple star system. We observe a series of frequencies at large
multiples of the orbital frequency in BW Aqr that we tentatively identify as
tidally induced pulsations in this well-studied eccentric binary system. We
find that the faint eclipsing binary EPIC201160323 shows rapid apsidal motion.
Rotational modulation signals are observed in 13 eclipsing systems, the
majority of which are found to rotate non-synchronously with their orbits. We
conclude that the K2 mission is a rich source of data that can be used to find
long period eclipsing binary stars. These data combined with follow-up
observations can be used to precisely measure the masses and radii of stars for
which such fundamental data are currently lacking, e.g., sub-giant stars and
slowly-rotating low-mass stars.
