5 citations · 15 across the 10 of their papers we have counts for
10 papers
A semiclassical theory of the chemical potential for the Atomic Elements
Bernard J. Laurenzi
The chemical potiential for the ground states of the atomic elements have been calculated within the semiclassical approximation The present work closely follows Schwinger and Engl…
Fourier Transform of some irrational integrands
Bernard J. Laurenzi
Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fre…
A Generalization of Fourier Series occurring in Atomic Theory
Bernard J. Laurenzi
A number of the Fourier Series which occur in the theory of the semi-classical atom due to Englert and Schwinger are generalized and presented.
Special values of the Lommel functions and associated integrals
Bernard J. Laurenzi
Special values of the Lommel functions allow the calculation of Fresnel like integrals. These closed form expressions along with their asymptotic values are reported.
Integrals containing the logarithm of the Airy Function Ai'(x)
Bernard J. Laurenzi
Integrals occurring in Thomas-Fermi theory which contains the logarithm of the Airy function Ai'(x) have been obtained in terms of analytical expressions.
Derivatives with respect to the order of the Legendre Polynomials
Bernard J. Laurenzi
Expressions for the derivatives of the Legendre polynomials of the first kind with respect to the order of these polynomials are given. An explicit form for the fourth derivative i…
Bessel and Struve Related Integrals
Bernard J. Laurenzi
Analytic expressions for integrals which arise in a theory of atomic structure due to Schwinger and Englert are evaluated in terms of Bessel and Struve functions
Logarithmic Integrals of Airy Functions
Bernard J. Laurenzi
Integrals arising in the Thomas-Fermi (TF) theory of atomic structure and which contain logarithms of the Airy functions have been expressed in terms of the incomplete Bell polynom…
Polynomials Associated with the Higher Derivatives of the Airy Functions Ai(z) and Ai'(z)
Bernard J. Laurenzi
The Airy function Ai(z) and its derivative Ai'(z) occur in a large number of applications in Chemistry and Physics. As a result, there is a continuing interest in the properties of…
Logarithmic Integrals, Polylogarithmic Integrals and Euler sums
Bernard J. Laurenzi
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.