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Table 4 The numerical results for \(\pmb{t=0.25}\)

From: Asymptotic expansions of the error for hyper-singular integrals with an interval variable

ex e n

\(\boldsymbol{2^{3}}\)

\(\boldsymbol{2^{4}}\)

\(\boldsymbol{2^{5}}\)

\(\boldsymbol{2^{6}}\)

\(\boldsymbol{2^{7}}\)

\(\boldsymbol{2^{8}}\)

\(\boldsymbol{2^{9}}\)

\(h^{0}-ex\)

3.600e − 2

1.240e − 2

4.286e − 3

1.490e − 3

5.202e − 4

1.823e − 4

6.405e − 5

\(r_{n}^{(0)}\)

 

21.5379

21.5326

21.5246

21.5178

21.5128

21.5091

\(h^{2}-ex\)

 

5.107e − 4

1.514e − 4

3.955e − 5

9.998e − 6

2.506e − 6

6.271e − 7

\(r_{n}^{(1)}\)

  

21.7538

21.9368

21.9840

21.9960

21.9990

\(h^{4}-ex\)

  

3.168e − 5

2.262e − 6

1.469e − 7

9.272e − 9

5.810e − 10

\(r_{n}^{(2)}\)

   

23.8081

23.9447

23.9855

23.9963