  A conjectured duality between supergravity and $N=\infty$ gauge theories
gives predictions for the glueball masses as eigenvalues for a supergravity
wave equations in a black hole geometry, and describes a physics, most relevant
to a high-temeperature expansion of a lattice QCD. We present an analytical
solution for eigenvalues and eigenfunctions, with eigenvalues given by zeroes
of a certain well-computable function $r(p)$, which signify that the two
solutions with desired behaviour at two singular points become linearly
dependent. Our computation shows corrections to the WKB formula $m^2= 6n(n+1)$
for eigenvalues corresponding to glueball masses QCD-3, and gives the first
states with masses $m^2=$ 11.58766; 34.52698; 68.974962; 114.91044; 172.33171;
241.236607; 321.626549, ... . In $QCD_4$, our computation gives squares of
masses 37.169908; 81.354363; 138.473573; 208.859215; 292.583628; 389.671368;
500.132850; 623.97315 ... for $O++$. In both cases, we have a powerful method
which allows to compute eigenvalues with an arbitrary precision, if needed so,
which may provide quantative tests for the duality conjecture. Our results
matches with the numerical computation of [5] well withing precision reported
there in both $QCD_3$ and $QCD_4$ cases. As an additional curiosity, we report
that for eigenvalues of about 7000, the power series, although convergent, has
coefficients of orders ${10}^{34}$; tricks we used to get reliably the function
$r(p)$, as also the final answer gets small, of order ${10}^{-6}$ in $QCD_4$.
In principle we can go to infinitely high eigenavalues, but such computations
maybe impractical due to corrections.
