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20 papers · 1 filter
On the asymptotic of Wright functions of the second kind
Richard Paris, Armando Consiglio, Francesco Mainardi
The asymptotic expansions of the Wright functions of the second kind, introduced by Mainardi [see Appendix F of his book {\it Fractional Calculus and Waves in Linear Viscoelasticit…
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…
A note on an extension of Gelfond's constant
A. K. Rathie, R. B. Paris
The aim of this note is to provide a natural extension of Gelfond's constant using a hypergeometric function approach. An extension is also found for the square root of this…
On a new result for the hypergeometric function
A. K. Rathie, R. B. Paris
The aim of this note is to provide a new identity connected with the Gauss hypergeometric function. This is achieved using results of certain combinatorial identities and a hyperge…
Asymptotics of the Mittag-Leffler function on the negative real axis when
R B Paris
We consider the asymptotic expansion of the single-parameter Mittag-Leffler function for as the parameter . The dominant expansion when consi…
Refined asymptotics of the Riemann-Siegel theta function
R. B. Paris
The Riemann-Siegel theta function is examined for . Use of the refined asymptotic expansion for $\log\,\g(z)$ shows that the expansion of …