Extended Error Expansion of Classical Midpoint Rectangle Rule for Cauchy Principal Value Integrals on an Interval

Table 3

Errors and convergence for the midpoint rectangle rule with .

32	3.5138e − 004	4.3272e − 004	2.4969e + 000	1.4503e + 000
64	9.7712e − 005	1.0842e − 004	2.4282e + 000	1.4065e + 000
128	2.5746e − 005	2.7122e − 005	2.3926e + 000	1.3837e + 000
256	6.6071e − 006	6.7814e − e − 006	2.3745e + 000	1.3721e + 000
512	1.6735e − 006	1.6954e − 006	2.3654e + 000	1.3662e + 000
1024	4.2110e − 007	4.2385e − 007	2.3608e + 000	1.3633e + 000
Convergence ratio	1.9409	1.9991	—	—