We provide here a complete integrability of the system of six coupled ODEs arising as reductions of the stratified Boussinesq equations by using WTC analysis. In this paper we have shown that among… (More)

We construct generalized Painlev e expansions with logarithmic terms for a general class of (`nonintegrable') scalar equations, and describe their structure in detail. These expansions were… (More)

We provide here a complete analysis of the system of six ODEs arising as reductions of the stratified Boussinesq equations. We demonstrate the complete integrability of this system and reduce the… (More)

In this paper we obtain explicit lower bounds for the radius of convergence of the Painlevé expansions of the Korteweg-de-Vries equation around a movable singularity manifold S in terms of the sup… (More)

A simple proof of Ramanujan’s formula for the Fourier transform of |Γ(a+ it)| is given where a is fixed and has positive real part and t is real. The result is extended to other values of a by… (More)