  We give an overview of our formalizations in the proof assistant Isabelle/HOL
of certain irrationality and transcendence criteria for infinite series from
three different research papers: by Erd\H{o}s and Straus (1974), Han\v{c}l
(2002), and Han\v{c}l and Rucki (2005). Our formalizations in Isabelle/HOL can
be found on the Archive of Formal Proofs. Here we describe selected aspects of
the formalization and discuss what this reveals about the use and potential of
Isabelle/HOL in formalizing modern mathematical research, particularly in these
parts of number theory and analysis.
