One of the formulas is given in [5, Theorem 1.1] and expressed as an infinite sum of which each

summand consists of the modified Bessel functions, the Gegenbauer polynomials and the densities [p.sub.r.sup(0)] (.;x).

where we just take the first

summand in the above infinite series when x is large.

when the elements [t.sub.i,j,l] are considered as elements of the direct

summand A of T or of the direct

summand C of T.

Let us consider the

summand [mathematical expression not reproducible].

leader of the house on Saturday in the Assembly session that already

summand by the Governor Balochistan, Muhammad Kahn Achakzai after receiving the summery sent by the Speaker Raheela Hameed Khan Durrani.Earlier Speaker Balochistan Assembly Wednesday asked Governor Balochistan to call provincial assembly session for electing new Leader of the House.

About Proposition [2.2], we have the following observation: if [mathematical expression not reproducible], when we compute every

summand of [a.sub.i][X.sub.i][b.sub.j][Y.sub.j] we obtain products of the coefficient [a.sub.i] with several evaluations of [b.sub.j] in [sigma]'s and [delta]'s depending of the coordinates of [[alpha].sub.i].

Noting that [xi]1 + [xi]1 [member of] R, we have [1/2]<1 + [[xi].sub.1]+[[xi].sub.1]< [3/2], and therefore the first

summand in (3.2) can be estimated as follows:

Since [mathematical expression not reproducible], the right-hand side of equality (6) and the second

summand of the left-hand side of this equality are divisible by [mathematical expression not reproducible].

For the

summand I1 we integrate by parts via identity

Consequently, the latter is also true for any orthogonal G-representation V without a trivial direct

summand, and it follows that the corresponding vector bundle EG x G V is integrally orientable.

The first

summand describes a comparative efficiency effect.

The last line in the chain of (34) resulted from fixing the random variable [Z.sub.k] in the kth

summand of the second line and then finding statistical expectation with respect to [Z.sub.k] in the kth

summand.