On the oscillation of the derivatives of a periodic function

1942/01/01 by George Pólya, Norbert Wiener · 2 citations
Mathematics · #Meromorphic and Entire Functions

paper · pdf · doi:10.1090/s0002-9947-1942-0007169-x

openalex publication_date 1942/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

Let f(x) be a real valued periodic function of period 2ir defined for all real values of x and possessing derivatives of all orders. Let Nk denote the number of changes of sign of /(W(x) in a period. We consider the order of magnitude of Nk as k-> oo.

Cited by

• On the zeros of the derivatives of a function and its analytic character
• George Pólya [wikipedia]