Derive_v5_05 / Derive / Users / SpecialFunctions / EulerMaclaurinSummation

File: EULERMAC.DOC     Euler-Maclaurin Summation Formula Documentation

EULERMAC.MTH was contributed by Jim FitzSimons of Cave Creek, Arizona.
Phone: [phone]  Fax: [phone]	E-mail: [e-mail]

The Euler-Maclaurin summation formula can be used to find asymptotic
expansions of finite or infinite sums.	It is described in Section 23.1.30
on page 806 of the Handbook of Mathematical Functions by Milton Abramowitz
and Irene A. Stegun.

Calls to EULERMAC as defined in EULERMAC.MTH should be of the form:

	EULERMAC(y,k,a0,a,b,m)

y should be an expression which is a function of k, the index variable of
the sum.  a0 and b are the starting and ending indexes of the sum,
respectively.  a is the start of the Euler-Maclaurin asymptotic expansion.
m is the order of the expansion.  a and m need to chosen large enough to
give the desired accuracy.

EULERMAC.DMO provides two examples using EULERMAC.