Exponential Gauss or Gauss–Hermite adjusted weights with
n odd and
.
Theoretically, in these cases:
- for , the central adjusted weight is infinite, and the exact function is zero at the central abscissa;
- for , the central adjusted weight is zero, and the exact function is infinite at the central abscissa.
In either case, the contribution of the central abscissa to the summation is indeterminate.
In practice, the central weight may not have overflowed or underflowed, if there is sufficient rounding error in the value of the central abscissa.
The weights and abscissa returned may be usable; you must be particularly careful not to ‘round’ the central abscissa to its true value without simultaneously ‘rounding’ the central weight to zero or as appropriate, or the summation will suffer. It would be preferable to use normal weights, if possible.
Note: remember that, when switching from normal weights to adjusted weights or vice versa, redefinition of is involved.