A new method of evaluating overlap integrals involving orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. For a large class of polynomials and for sufficiently large orders, these coefficients can be written explicitly as Taylor series in terms of powers of = 1/n, where n is the polynomial order. Such decompositio...

A technique for avoiding infinite integrals in the calculation of the one-loop diagram contribution to the vacuum polarization component of an atomic energy level is presented. This makes renormalization unnecessary. Infinite integrals do not occur because, as it is shown, no delta functions are required for the Green’s functions. Thus there are none to overlap. This procedure is shown to produ...

A technique for avoiding infinite integrals in the calculation of the one-loop diagram contribution to the vacuum polarization component of an atomic energy level is presented. This makes renormalization unnecessary. Infinite integrals do not occur because, as it is shown, no delta functions are required for the Green’s functions. Thus there are none to overlap. This procedure is shown to produ...

We have used computer algebra CA to tabulate closed expressions for over lap integrals of Slater orbitals with principal quantum numbers to con taining symbolic molecular parameters Also we have constructed precise closed expressions for a range of overlap integrals de ned by higher quantum numbers and numerical bond lengths and or screening constants Numerical values obtained from both sets of...

in this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by boundary elements. the integrals in boundary integrals equations are inherently singular. for example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

The rapid evaluation of two-center Coulomb and overlap integrals between contracted auxiliary solid harmonic Gaussian functions is examined. Integral expressions are derived from the application of Hobson's theorem and Dunlap's product and differentiation rules of the spherical tensor gradient operator. It is shown that inclusion of the primitive normalization constants greatly simplifies the c...

The first diagonalization step in a rho-axis-method treatment of methyl-top internal rotation problems involves finding eigenvalues and eigenvectors of a torsional Hamiltonian, which depends on the rotational projection quantum number K as a parameter. Traditionally the torsional quantum number vt = 0, 1, 2···is assigned to eigenfunctions of given K in order of increasing e...

One of the important parameters that determine the performance of the FEL is the overlap between electron beam and radiation field during the amplification process. An earlier study has shown that in order to maintain this overlap, quadrupoles have to be aligned with an accuracy of 1 m. In addition, first and second field integrals of the magnetic structures have to be corrected. Since this can...

In this contribution we define a new class of non-linear integrals based on decomposition integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is prov...

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...