x

$\pi \left(\sqrt{x}\right)$

$\pi \left(\sqrt{2}x\right)$

${\mathbb{A}}_1\left(x\right)$

${{\mathbb{A}}^{″}}_1\left(x\right)$

${{\mathbb{A}}^{\prime }}_1\left(x\right)$

${\mathbb{K}}_1\left(x\right)$

${\mathbb{K}}_2\left(x\right)$

$\pi \left[x\mathrm{,2}x\right]$

${{\mathbb{K}}^{\prime }}_1\left(x\right)$

${{\mathbb{K}}^{\prime }}_2\left(x\right)$

$\mu$

${\mu }^{\prime }$

$\frac{\mu \left(\mu -1\right)}{2}$

$\frac{{\mu }^{\prime }\left({\mu }^{\prime }-1\right)}{2}$

${{\mathbb{A}}^{″}}_1\left(x\right)-{\mathbb{A}}_1\left(x\right)$

$\pi \left(x\right)-{\mathbb{A}}_1\left(x\right)$

$\pi \left(x\right)-{{\mathbb{A}}^{\prime }}_1\left(x\right)$

(%error)

(%error)

10

2

2

1

1

0

3

4

4

1

0

(25)

(0)

10²

4

6

6

15

9

19

16

21

2

5

(9.5)

(23.8)

10³

11

14

55

91

36

113

132

135

22

3

(16.3)

(2.2)

10⁴

25

34

300

561

261

929

968

1033

104

65

(10.1)

(6.3)

10⁵

65

86

2080

3655

1575

7512

8017

8392

880

375

(10.4)

(4.6)

10⁶

168

223

14,028

24,753

10,725

64,470

67,773

70,435

5965

2662

(8.4)

(3.8)