The authors discuss the multiple (actually double) zeros of the first to third derivatives of
with real parameter
. They first refer previous works since J. Lense (1932/33). Due to Bessel’s differential equation and its derivatives, we have easily a necessary condition and asymptotic formulas of z and
for double zeros of the functions
. Starting from the asymptotic value in each interval between two consecutive integers
, they compute the numerical values of
and z, using Taylor expansion in two variables
and z. They also give several tables for the results.