Figure 19.3.6 (See in context.)3DHelpFigure 19.3.6:
as a function of and
for , .
Cauchy principal values are shown when
.
The function tends to as ,
except in the last case below.
If (), then the function reduces to
with Cauchy principal value
,
which tends to as .
See (19.6.5) and (19.6.6).
If (), then by (19.7.4)
it reduces to , ,
with Cauchy principal value
,
, by (19.6.5).
Its value tends to as by
(19.6.6), and to the negative of the second lemniscate
constant (see (19.20.22)) as
.
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