Bessel turning-point asymptotic
= Bessel turning-point asymptotic
{c}
{title2=$J_n(n)\sim 2^{1/3}n^{-1/3}/[3^{2/3}\Gamma(2/3)]$}
At equal argument and large integer order, the <Bessel function of the first kind> has phase $n(\sin t-t)=-nt^3/6+\cdots$ near the endpoint. The <cubic stationary endpoint> yields the displayed positive constant. It is also the zero-argument value of the <Airy function> in the uniform Bessel turning-point approximation.