eulermac
Euler-Maclaurin summation
Calling Sequence
Parameters
Description
Examples
eulermac(expr, x) or eulermac(expr, x = a..b)
eulermac(expr, x, n) or eulermac(expr, x = a..b, n)
expr
-
expression in x
x
independent variable
a, b
interval over which the approximation to the sum is computed
n
(optional) integer (degree of summation)
The forms eulermac(expr, x) and eulermac(expr, x, n) compute asymptotic approximations to sum(expr, x). If F(x) = eulermac(f(x), x), then Fx+1−Fx is asymptotically equivalent to f(x). The order of the approximation is specified by n, and defaults to Order - 1.
The forms eulermac(expr, x=a..b) and eulermac(expr, x=a..b, n) compute nth degree Euler-Maclaurin summation formulas for expr (thus n terms of the expansion are given). If n is not specified, it is assumed to be Order - 1.
eulermac1x,x
lnx−12x−112x2+1120x4−1252x6+O1x8
eulermac1k,k=1..x
∫1x1kⅆk+γ+12x−112x2+1120x4−1252x6+O1x8
eulermac1x2,x
−1x−12x2−16x3+130x5−142x7+O1x9
eulermac1k2,k=1..x,4
∫1x1k2ⅆk+π26−1+12x2−16x3+130x5+O1x7
See Also
sum
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