Table 1 The absolute error for Example 7.1 for different estimations of \(k, M\) at \(\alpha=1\)

0.1

1.6403 × 10⁻⁷

1.4281 × 10⁻⁹

2.0695 × 10⁻¹⁰

1.574 × 10⁻¹²

4.2461 × 10⁻¹⁴

0.2

2.5018 × 10⁻⁷

2.7054 × 10⁻⁹

4.1957 × 10⁻¹⁰

2.1255 × 10⁻¹²

5.0451 × 10⁻¹⁴

0.3

1.4102 × 10⁻⁷

4.7082 × 10⁻⁹

1.4795 × 10⁻¹⁰

2.1443 × 10⁻¹²

2.6821 × 10⁻¹⁴

0.4

2.1512 × 10⁻⁷

6.5014 × 10⁻⁹

3.1759 × 10⁻¹⁰

3.1682 × 10⁻¹²

3.5171 × 10⁻¹⁴

0.5

1.9018 × 10⁻⁷

2.7802 × 10⁻⁹

5.6087 × 10⁻¹⁰

4.6833 × 10⁻¹²

2.6417 × 10⁻¹⁴

0.6

4.4186 × 10⁻⁷

2.3081 × 10⁻⁹

2.2781 × 10⁻¹⁰

3.6951 × 10⁻¹²

1.7129 × 10⁻¹³

0.7

3.1042 × 10⁻⁶

4.2721 × 10⁻⁸

1.7309 × 10⁻⁹

1.2071 × 10⁻¹¹

2.6357 × 10⁻¹³

0.8

4.3051 × 10⁻⁶

1.3062 × 10⁻⁸

2.9053 × 10⁻⁹

2.2721 × 10⁻¹¹

3.6457 × 10⁻¹³

0.9

3.2101 × 10⁻⁶

2.3775 × 10⁻⁸

2.0941 × 10⁻⁹

3.2974 × 10⁻¹¹

1.6864 × 10⁻¹³