Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders

a re sought for la rge values of IILI, which a re uniformly valid wi th respect Lo a rg IL and un restricted va lues of the complex variable t. Two types of expa nsion are found . Those of the first type are in terms of elementary func t ions and are valid outside t he neighborhoods of t he poi nts t= ± 1, t he t urning poin ts of t he differe nt ial equation . The second a re in terms of Airy functions and hold in unbounded regions co ntaining one of t he t urnin g poin ts. The special forms of t he expansions when t he va riab les are real a rc considered in detail , and asymp to tic ex pans ions for t he ze ros of solu t ions of t he different ia l equation a re found by reversion. N umerical examples are in cluded .