  The family of quads of interrelated functions holomorphic on the universal
cover of the complex plane without zero (for brevity, pqrs-functions),
revealing a number of remarkable properties, is introduced. In particular,
under certain conditions the transformations of the argument $z$ of
pqrs-functions represented by lifts of the replacements $ z \leftarrow -1/z $ $
z \leftarrow -z $, and $ z \leftarrow 1/z $ are equivalent to linear
transformations with known coefficients. Pqrs-functions arise in a natural way
in constructing of certain linear operators acting as automorphisms on the
space of solutions to the special double confluent Heun equation (sDCHE).
Earlier such symmetries were known to exist only in the case of integer value
of one of the constant parameters when the predecessors of pqrs-functions
appear as polynomials. In the present work, leaning on the generalized notion
of pqrs-functions, discrete symmetries of the space of solutions to sDCHE are
extended to the general case, apart from some natural exceptions.
