S ev/od const 5 linear polynomials in x~ cubic polynomials in x] -4
0 Po5 + o5 + 7-
Po Po Po
(5-163)
where x" denotes the Schwarzschild coordinates (t, r, 0, 0). Eq. (5-163) has the
expansion basis d2Pe(X)/dX2, and C-5-term and C-4-term here would correspond to
C-l-term and co-term of the expansion with the basis Pe(X) as in Eq. (5-72), since
the weighting function (1 X2)2 s= in4 e p1 1-ing into Eqs. (5-149), (5-150) and
(5-151) makes up for e4 in the limit O -- 0. Structure analyses for C-5-term and
C-4-term may be developed in a similar manner to that in Section 4.4 so that we
can find the non-vanishing regularization parameters via Eqs. (5-160) and (5-161).
The other cases for h, and hs, can be treated in the same manner as above.
The results of the calculations are
,S ( ....Trace ev od ( ....Trace v )
Tae = Bce + B^ + Be) + ee + Cee + ce) + O( 2) (5-164)
0 Tra = e + B +ev + od) (CTace + C o ) + O( 2) (5-165)
hs B.Trace + v od, ae + + (f-2od), I-1
B B C = B + B + B) 6) + + Trace ) (5-166)
h, (BTrace fTTrace e