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.
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.