  Elementary, but very useful lemma due to Biernacki and Krzy\.{z} (1955)
asserts that the ratio of two power series inherits monotonicity from that of
the sequence of ratios of their corresponding coefficients. Over the last two
decades it has been realized that, under some additional assumptions, similar
claims hold for more general series ratios as well as for unimodality in place
of monotonicity. This paper continues this line of research: we consider ratios
of general functional series and integral transforms and furnish natural
sufficient conditions for preservation of unimodality by such ratios. Numerous
series and integral transforms appearing in applications satisfy our sufficient
conditions, including Dirichlet, factorial and inverse factorial series,
Laplace, Mellin and generalized Stieltjes transforms, among many others.
Finally, we illustrate our general results by exhibiting certain statements on
monotonicity patterns for ratios of some special functions. The key role in our
considerations is played by the notion of sign regularity.
