ANALYTIC AND ASYMPTOTIC PROPERTIES OF LINNIKS PROBABILITY DENSITIES


HAYFAVI A., KOTZ S., OSTROVSKII I.

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, cilt.319, ss.985-990, 1994 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 319 Konu: 9
  • Basım Tarihi: 1994
  • Dergi Adı: COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
  • Sayfa Sayıları: ss.985-990

Özet

The analytic and asymptotic properties of the probability density p(alpha) (x) introduced in 1953 by Ju. V. Linnik and defined by the characteristic function 1/(1 + \t\(alpha)), 0 < alpha < 2, are studied. Expansions of p(alpha) (x) into convergent and asymptotic series in terms of log \x\, \x\(k alpha) , \x\(k) (k = 0, 1, 2,...) are obtained. It turns out that the analytic structure of p(alpha) (x) depends substantially on the arithmetical nature of the parameter alpha.