Figure 19.3.6 (See in context.)

Figure 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 .