Details and Options
The expression expr must be numeric when its argument z is numeric.
ResourceFunction["NLimit"] constructs a sequence of values that approach the point z0 and uses extrapolation to find the limit.
is unable to recognize small numbers that should in fact be zero. Chop
may be needed to eliminate these spurious residuals.
ResourceFunction["NLimit"] often fails when the limit has a power law approach to infinity.
The following options can be given:
|WorkingPrecision||MachinePrecision||precision to use in internal computations|
|Direction||Automatic||vector giving the direction of approach|
|"Scale"||1||initial step size in the sequence of steps|
|"Terms"||7||number of terms used to evaluate the limit|
|Method||"EulerSum"||the method used to evaluate the result|
|"WynnDegree"||1||degree used in Wynn's epsilon algorithm|
The option Direction→d
specifies that the approach vector to a finite limit point z0
is given by the complex number d
. The default setting Direction→Automatic
is equivalent to Direction→-1
, and computes the limit as z
from larger values.
ResourceFunction["NLimit"] approaches infinite limit points on a ray from the origin.
The option "Scale" specifies the initial step in the constructed sequence.
For finite limit points x0, the initial step is a distance "Scale" away from x0. For infinite limit points, the initial step is a distance "Scale" away from the origin.
The accuracy of the result is generally improved by increasing the number of terms, although increased WorkingPrecision
will also usually be necessary.
Possible settings for Method
|"EulerSum"||converts sequence to a sum|
|"SequenceLimit"||constructs a sequence|
The option "WynnDegree" specifies the number of iterations of Wynn's epsilon algorithm to be used by "SequenceLimit". In general, there must be at least 2(n+1) terms for n iterations.