Using

integrands of gamma and beta functions, the gamma and beta density functions are usually defined.

Since the semigroup is compact, and the

integrands are dominated by an integrable process (due to Corollary 3.

zz] cannot be evaluated analytically since it involves nonintegrable

integrands.

The tables are organized in a logical manner with standard forms of

integrands arranged in increasing order of complexity, ranging from algebraic forms to special functions and combinations.

Generally, we omit the t-dependence of the

integrands in the notation.

In the course of these calculations, two rather complex integrals appear, involving

integrands which are trigonometric functions raised to fractional powers; however, we were able to evaluate them, and this allowed the determination of a valid first-order approximation to the solution, i.

The major difficulty in using the vector potential to analyse NMHA is that the

integrands cannot be separated in general coordinate systems [6].

It turns out that for evaluation of the corresponding integrals, it is more convenient to distort the integration path in the complex p plane so as to enclose all poles and branch singularities of the

integrands and then choose the quantity q defined by Equation (18) as an integration variable.

where one of the

integrands can be written by means of series as follows:

The square brackets in the triple integrals in (2) indicate that the

integrands [[rho]/r"] and [[rho]u/r"] are to be integrated over the volume of the central object at the retarded time.

From Equations (40), (46) and Figure 7, we see that the highly oscillatory

integrands defined on the three edges of the triangular patch are [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

This high quality of numerical integration is not surprising, given the smoothness of the

integrands in every dimension.