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Table 1 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

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

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

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

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

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

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

\(h^{0}-ex\)

2.331e − 2

6.077e − 3

1.573e − 3

3.854e − 4

9.643e − 5

2.411e − 5

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

 

21.9395

21.9833

21.9957

21.9989

21.9997

\(h^{2}-ex\)

 

3.329e − 4

2.363e − 5

1.533e − 6

9.696e − 8

6.065e − 9

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

  

23.8163

23.9463

23.9859

23.9964

\(h^{4}-ex\)

  

3.014e − 6

5.972e − 8

1.004e − 9

1.597e − 11

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

   

25.6571

25.8942

25.9745

\(h^{6}-ex\)

   

1.284e − 8

7.213e − 11

2.800e − 13