Table 3 Numerical results of \(\Gamma _{ q}(\theta + \vartheta + \lambda +1)\), \(\Gamma _{ q}(\theta + \vartheta + \lambda )\), \(\Gamma _{ q}( \lambda + 1)\), \(\Gamma _{ q}(\theta + \vartheta +1)\), \(\Gamma _{ q}(\theta + \vartheta )\), \(\Gamma _{ q}(\theta + \vartheta + \lambda -\mu +1)\), \(\Gamma _{ q}(\theta + \vartheta + \lambda -\mu )\), \(\Gamma _{ q}(\theta -\mu +1)\), and \(\aleph _{1}\), \(\aleph _{2}\) of \(\mathbb{F}\mathrm{D}q-\mathbb{DP}\) (24) with \(q=\frac{8}{9}\)

1

67.0460

15.4708

7.4364

26.5870

8.4220

0.0832

2

48.4129

13.5941

8.3916

21.4361

8.6345

0.0938

3

38.0888

12.3894

9.1229

18.3336

8.7868

0.1038

⋮

⋮

⋮

⋮

⋮

⋮

⋮

71

11.8035

8.0386

13.1855

8.7147

9.5062

0.1925

72

11.8032

8.0385

13.1856

8.7146

9.5063

73

11.8028

8.0384

13.1857

8.7144

9.5063

0.1926

⋮

⋮

⋮

⋮

⋮

⋮

⋮

79

11.8016

8.0381

13.1861

8.7138

9.5063

0.1926

80

11.8014

8.0381

13.1862

8.7138

9.5064

0.1926

81

11.8013

8.0380

13.1862

8.7137

9.5064

0.1926

⋮

⋮

⋮

⋮

⋮

⋮

⋮

93

11.8006

8.0379

13.1864

8.7134

9.5064

0.1926

94

11.8005

8.0379

13.1865

8.7133

9.5064

0.1926

95

11.8005

8.0378

13.1865

8.7133

9.5064

0.1926

96

11.8005

8.0378

13.1865

8.7133

9.5064

0.1926

1

45.0140

11.5522

8.4748

0.0287

2

33.9505

10.7796

10.4335

0.0363

3

27.6133

10.2616

12.0231

0.0435

⋮

⋮

⋮

⋮

⋮

65

10.1749

8.1827

22.2055

0.1103

66

10.1744

8.1826

22.2062

67

10.1739

8.1825

22.2067

0.1104

⋮

⋮

⋮

⋮

⋮

82

10.1709

8.1820

22.2106

0.1104

83

10.1708

8.1819

22.2107

0.1104

⋮

⋮

⋮

⋮

⋮

94

10.1704

8.1819

22.2112

0.1104

95

10.1704

8.1819

22.2113

0.1104

96

10.1703

8.1819

22.2113

0.1104

97

10.1703

8.1819

22.2113

0.1104