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M2X translation formula
Using (3.22), (4.2), (B.1), (B.2)
and the following identity:
we obtain
where X(k,j;O) is the coefficient of the exponential expansion centred
at O defined as



(J.1) 
Exchanging an order of the double sum in (J.1) (See Fig.J.1) we
rewrite (J.1) as



(J.2) 
Figure J.1:
Exchange of indices

Next we estimate the cost for M2X translation.
Noting (J.2) and truncating the infinite series
(3.22) with p terms, the cost can be roughly
estimated as follows:
where C_{0} and C_{1} are the computational cost related to
and
in
(J.2), respectively and C_{2} is the negligible cost.
Next: X2X translation formula
Up: M2X, X2X, X2L in
Previous: M2X, X2X, X2L in
Kenichi Yoshida
20010728