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Table 1 Numerical values of \(\pmb{\mu_{1} = k \Vert \mathcal{K}_{l, \alpha, k} \Vert }\) , \(\pmb{\nu_{1}}\) , \(\pmb{\mu_{2}}\) , \(\pmb{\nu_{2}}\) corresponding to various \(\pmb{L = 2l\alpha}\)

From: Spectral analysis of the integral operator arising from the beam deflection problem on elastic foundation II: eigenvalues

L

\(\boldsymbol{\mu_{1}}\)

\(\boldsymbol{\nu_{1}}\)

\(\boldsymbol{\mu_{2}}\)

\(\boldsymbol{\nu_{2}}\)

10−2

0.003535504526434

0.000000029355791

0.000000000019880

0.000000000002624

10−1

0.035326704321880

0.000028406573449

0.000000190403618

0.000000025815905

1

0.331681981441542

0.020235634105536

0.001302361278230

0.000221108040807

2

0.578350951060946

0.109509249925520

0.014548864439394

0.003014813082734

3

0.737796746567301

0.249144755528815

0.052681487593071

0.013049474696160

4

0.835237998797342

0.400500295380442

0.119710823211630

0.035118466933057

5

0.894054175695477

0.537478928105431

0.209949500302561

0.072359812095134

6

0.929940126283050

0.649631031236143

0.312512968129316

0.125219441432141

7

0.952321667263849

0.736387662150921

0.416408511420210

0.191399578520264

8

0.966653810417898

0.801474122928057

0.513537323059282

0.266679190778082

9

0.976084258929463

0.849614047989366

0.599392090820732

0.346127057405707

10

0.982453999322008

0.885083551582694

0.672409494807652

0.425184184899229

102

0.999995523152271

0.999965988373225

0.999869326766519

0.999643102015955