Table 2 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 \(q=\frac{1}{2}\)

1

2.8428

1.9971

2.4929

2.2164

2.0510

1.1087

2

2.6015

1.9154

2.6121

2.0773

2.0696

1.1497

3

2.4936

1.8780

2.6690

2.0144

2.0783

1.1710

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9

2.3945

1.8431

2.7233

1.9562

2.0866

1.1924

10

2.3938

1.8429

2.7237

1.9558

2.0867

1.1926

11

2.3934

1.8427

2.7239

1.9556

2.0867

1.1927

12

2.3932

1.8427

2.7240

1.9554

2.0867

1.1927

13

2.3931

1.8426

2.7241

1.9554

2.0867

1.1927

14

2.3930

1.8426

2.7241

1.9554

2.0867

15

2.3930

1.8426

2.7241

1.9554

2.0867

1.1928

16

2.3930

1.8426

2.7241

1.9553

2.0867

1.1928

17

2.3930

1.8426

2.7241

1.9553

2.0867

1.1928

1

2.5368

1.9488

3.6511

0.6997

2

2.3418

1.9037

3.9742

0.7367

3

2.2542

1.8829

4.1309

0.7561

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11

2.1726

1.8631

4.2842

0.7760

12

2.1725

1.8631

4.2845

13

2.1724

1.8631

4.2846

0.7761

14

2.1724

1.8630

4.2847

0.7761

15

2.1724

1.8630

4.2847

0.7761

16

2.1723

1.8630

4.2848

0.7761

17

2.1723

1.8630

4.2848

0.7761