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 .
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.