For the th positive zeros of , , , and are denoted by , , , and , respectively, except that for we count as the first zero of .
With the notation of §10.21(i),
Hence properties of and are derivable straightforwardly from results given in §§10.21(i)–10.21(iii), 10.21(vi)–10.21(viii), and 10.21(x). However, there are no simple relations that connect the zeros of the derivatives. For some properties of and , including asymptotic expansions, see Olver (1960, pp. xix–xxi).