arXiv subjects
Publications and source records attributed to 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 Englert's semiclassical treatment of atomic structure.
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 Fresnel integrals. Such integrals arise in the semi-classical theory of the Chemical Potential of the atomic elements.
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 allow the calculation of Fresnel like integrals. These closed form expressions along with their asymptotic values are reported.
Integrals occurring in Thomas-Fermi theory which contains the logarithm of the Airy function Ai'(x) have been obtained in terms of analytical expressions.
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 is presented.
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
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 polynomials. In keeping with the spirit of TF theory closed forms for these integrals are sought.
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 these functions. Recently, there has been interest in obtaining general expressions for the higher derivatives of these functions. In this work, general expressions for the polynomials which are contained in these derivatives are given in terms of the partial Bell polynomials.
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.