  Digital mathematical libraries assemble the knowledge of years of
mathematical research. Numerous disciplines (e.g., physics, engineering, pure
and applied mathematics) rely heavily on compendia gathered findings. Likewise,
modern research applications rely more and more on computational solutions,
which are often calculated and verified by computer algebra systems. Hence, the
correctness, accuracy, and reliability of both digital mathematical libraries
and computer algebra systems is a crucial attribute for modern research.
  In this paper, we present a novel approach to verify a digital mathematical
library and two computer algebra systems with one another by converting
mathematical expressions from one system to the other. We use our previously
eveloped conversion tool (referred to as LaCASt) to translate formulae from the
NIST Digital Library of Mathematical Functions to the computer algebra systems
Maple and Mathematica. The contributions of our presented work are as follows:
(1) we present the most comprehensive verification of computer algebra systems
and digital mathematical libraries with one another; (2) we significantly
enhance the performance of the underlying translator in terms of coverage and
accuracy; and (3) we provide open access to translations for Maple and
Mathematica of the formulae in the NIST Digital Library of Mathematical
Functions.
