Based on known properties of the asymptotic expansion, we consider the pair wise interrelation of values x, N, and \ Delta.
42.
This equation contains two terms of the asymptotic expansion of E \ tau and 2 \ epsilon is the angle of the absorbing boundary.
43.
Where is the th Bernoulli number ( note that the infinite sum is not convergent, so this formula is just an asymptotic expansion ).
44.
The above asymptotic expansion of the angular momentum l ( K ) in descending powers of K can also be derived with the WKB method.
45.
A more accurate approximation can be obtained by using more terms from the asymptotic expansions of and, which are based on Stirling's approximation.
46.
Note that although the generalized Lambert W function eigenvalue solutions supersede these asymptotic expansions, in practice, they are most useful near the bond length.
47.
The case \ beta close to 1 remains open, and for general domains, the asymptotic expansion of the escape time remains an open problem.
48.
In 2005, the topological asymptotic expansion for the Laplace equation with respect to the insertion of a short crack inside a plane domain had been found.
49.
Thus, at a given x, the exactness first increases with the growth of N and then decreases ( so one has an asymptotic expansion ).
50.
When it does not converge, the series is also not a true asymptotic expansion, because it is not possible to estimate the error of the expansion.
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