4 papers
Lehmer-Lambert Distribution
Masoud Ataei, Vladimir V. Vinogradov
The Lehmer transform of a positive signal is the ratio of its power sums at consecutive orders, read as a function of the order, and it is a strictly increasing analytic curve from…
Some analytical results associated with extensions of the canonical Feller-Spitzer distribution
R. B. Paris, V. V. Vinogradov
In this work, we establish new analytical results which are required for the derivation of subtle properties of the members of two classes of the generalized Feller--Spitzer distri…
The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton-Watson processes
R B Paris, Vladimir V Vinogradov
We evaluate the sum of Gauss hypergeometric functions \[S(μ,c;x)=\sum_{k\geq 0} \bl(\frac{1-x}{1+μ}\br)^k\,{}_2F_1(\fs k+\fs, \fs k+1;c;x)\] for and positive paramete…
Asymptotic and structural properties of special cases of the Wright function arising in probability theory
R. B. Paris, V. Vinogradov
This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and th…