Analytic and asymptotic properties of Linnik's probability densities
Ostrovskii, I. V.
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
985 - 990
Item Usage Stats
MetadataShow full item record
The analytic and asymptotic properties of the probability density Jin (:r:) introduced in 1953 by Ju. V. Linnik and defined by the characteristic function 1/(1 + It I"), 0 < n < 2, are studied. Expansions of Jin (:r:) into convergent and asymptotic series in terms of log I :r: I , I x I k n, I ,r I k (k = 0, 1, 2, ... ) are obtained. It turns out that the analytic structure of Pc, (:r:) depends substantially on the arithmetical nature of the parameter n.