Table 2 Numerical values of \(\pmb{\beta_{n}}\) and \(\pmb{\gamma_{n}}\) when \(\pmb{L = 1}\)
n | Name | Value | (2 π ( n − 1)∓ π /2)/ L |
|---|---|---|---|
1 | \(h^{-1}(2\pi- \pi/2)\) | 1.158670738392296 | |
\(\beta_{1}\) | 1.191421197714390 | −1.570796326794896 | |
\(h^{-1}(2\pi)\) | 1.750980760482237 | ||
\(\gamma_{1}\) | 2.637856739191656 | 1.570796326794896 | |
\(h^{-1}(2\pi+ \pi/2)\) | 2.673553841718542 | ||
2 | \(h^{-1}(4\pi- \pi/2)\) | 5.256787217675680 | |
\(\beta_{2}\) | 5.262300407849289 | 4.712388980384689 | |
\(h^{-1}(4\pi)\) | 6.707921416840514 | ||
\(\gamma_{2}\) | 8.200207778135508 | 7.853981633974483 | |
\(h^{-1}(4\pi+ \pi/2)\) | 8.200581481509233 | ||
3 | \(h^{-1}(6\pi- \pi/2)\) | 11.247700835446595 | |
\(\beta_{3}\) | 11.247720678493973 | 10.995574287564276 | |
\(h^{-1}(6\pi)\) | 12.787998043974640 | ||
\(\gamma_{3}\) | 14.334797074430887 | 14.137166941154069 | |
\(h^{-1}(6\pi+ \pi/2)\) | 14.334798038235459 | ||
4 | \(h^{-1}(8\pi- \pi/2)\) | 17.441107108879219 | |
\(\beta_{4}\) | 17.441107153760840 | 17.278759594743862 | |
\(h^{-1}(8\pi)\) | 18.998568977749238 | ||
\(\gamma_{4}\) | 20.558043111829927 | 20.420352248333656 | |
\(h^{-1}(8\pi+ \pi/2)\) | 20.558043113872500 | ||
5 | \(h^{-1}(10\pi- \pi/2)\) | 23.681452204590053 | |
\(\beta_{5}\) | 23.681452204681734 | 23.561944901923449 | |
\(h^{-1}(10\pi)\) | 25.244839588317457 | ||
\(\gamma_{5}\) | 26.809088990153228 | 26.703537555513242 | |
\(h^{-1}(10\pi+ \pi/2)\) | 26.809088990157306 |