ANALYTIC AND ASYMPTOTIC PROPERTIES OF LINNIKS PROBABILITY DENSITIES

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HAYFAVI A., KOTZ S., OSTROVSKII I.

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, vol.319, no.9, pp.985-990, 1994 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 319 Issue: 9
• Publication Date: 1994
• Journal Name: COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
• Page Numbers: pp.985-990
• Middle East Technical University Affiliated: No

Abstract

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.