For a general d, Zhao [12] proved the analytic continuation of [zeta]([s.sub.1], ..., [s.sub.d]) as a function of d variables using the theory of generalized function and Akiyama, Egami and Tanigawa [1] proved the same result by applying the classical
Euler-Maclaurin formula to the index of the summation [n.sub.d].
In this note we have illustrated applications of the Euler-Maclaurin formula to the estimation of graph entropies of paths and rings.
[9] __, The Euler-Maclaurin formula and sums of powers revisited, Int.
Balanzario, "A generalized
Euler-Maclaurin formula for the Hurwitz zeta function," Mathematica Slovaca, vol.
In order to evaluate this function, we use the
Euler-Maclaurin formula defined as follows:
With the Euler-Maclaurin formula, Moak [6] obtained the following q-analogue of Stirling formula
In this paper, the Euler-Maclaurin formula is exploited to provide an expression for the q-factorial function as an infinite integral.
In mathematics, the Euler-Maclaurin formula provides a powerful connection between integrals and sums.
In the context of computing asymptotic expansions of sums and series, usually the most useful form of the Euler-Maclaurin formula is
(15), however, the
Euler-Maclaurin formula may be used to obtain a more easily evaluated, asymptotic expression for Q(A):
Also, it introduces the new q-operator to reach the q-analogue of
Euler-Maclaurin formula.
The
Euler-MacLaurin formula. Let m [greater than or equal to] 0, n [greater than or equal to] 1, and define h = (b - a) /n, [x.sub.j] = a + jh for j = 0, 1, ..., n.
