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Table 2 Positive zeroes of \(\mathtt{W}_{ \nu , 1}^{\mathtt{k}}\) for different ν and k

From: Differential equation and inequalities of the generalized k-Bessel functions

ν

−0.4

−0.3

0

0.5

1

1.5

2

2.5

k = 0.5 and c = 1

1st zero

0.662422

0.97534

1.70047

2.70943

3.63143

4.51146

5.36577

6.20238

2nd zero

2.96686

3.21271

3.90328

4.96077

5.95189

6.90209

7.82393

8.72471

3rd zero

5.2018

5.43751

6.11911

7.19373

8.21647

9.20314

10.1629

11.1017

k = 1 and c = 1

1st zero

1.75098

1.92285

2.40483

3.14159

3.83171

4.49341

5.13562

5.76346

2nd zero

4.87852

5.04213

5.52008

6.28319

7.01559

7.72525

8.41724

9.09501

3rd zero

8.01663

8.17785

8.65373

9.42478

10.1735

10.9041

11.6198

12.3229

k = 1.5 and c = 1

1st zero

2.42334

2.55767

2.9453

3.55493

4.13426

4.69286

5.2362

5.76774

2nd zero

6.24148

6.37291

6.76069

7.38858

7.9979

8.5923

9.1744

9.74613

3rd zero

10.0812

10.2116

10.5986

11.2315

11.8513

12.4599

13.0587

13.6488

k = 2 and c = 1

1st zero

2.95334

3.06754

3.40094

3.93277

4.44288

4.93703

5.41885

5.8908

2nd zero

7.3588

7.47176

7.80657

8.35255

8.88577

9.40825

9.92154

10.4269

3rd zero

11.7913

11.9037

12.2382

12.7879

13.3286

13.8616

14.3875

14.907