Proved. The site labels the problem PROVED (page last edited 19 October 2025) and credits Lewis, Rossi and Weitsman [LRW84] with the general case, after Zhang [Zh77] had settled the entire functions of finite order and Huber [Hu57] had found, for each fixed $\lambda$, a path on which that one integral is finite. The accepted claim page Lewis, Rossi and Weitsman 1984 records the result, on the refereed venue and the site's acceptance; the frontmatter standing derives from it. Zhang's finite-order case is the accepted partial claim Zhang 1977, on its journal publication.