Hertz to mel conversion is computed according to:
$$m = 1127.01048 \times {\log{(1+(\frac{f}{700}))}}$$
with m in Mel and f in Hertz.
Mel to Hertz conversion (when inverse is TRUE)
is therefore computed according to:
$$f = 700 \times{(e^{\frac{m}{1127.01048}}-1)}$$
with f in Hertz and m in Mel.
References
Stevens, S. S., Volkman, J. and Newman, E. B. 1937.
A scale for the measurement of psychological magnitude pitch.
Journal of the Acoustical Society of America, 8: 185-190.