Asymptotics of the uniform norm of associated Legendre functions <i>P</i><sup><i>k</i></sup><sub><i>n</i></sub> (the case <i>k</i> ≪ <i>n</i>)
Kholshevnikov K.V., Shaidulin V.Sh. Asymptotics of the uniform norm of associated Legendre functions P kn (the case k 2/3, is considered. It is obtained that the norm increases as nk. A corresponding coefficient is equal to the greatest value of the Bessel function of order k. The asymptotics of the coefficient is also established: decreasing as k-1//3 with an exact numerical coefficient. Direct calculations show that the asymptotic approximation is satisfactory even for the first small values of the superscript.