Table 3 Numerical values of \(\pmb{\mu_{n}}\) and \(\pmb{\nu_{n}}\) when \(\pmb{L = 1}\)
n | Name | Value | \(\boldsymbol{1/ \{ 1 + ( 2\pi(n-1) \mp\pi/2 )^{4}/L^{4} \}}\) |
|---|---|---|---|
1 | \(1/ \{1 + ( h^{-1}(2\pi- \pi/2) )^{4} \}\) | 0.356842821387149 | |
\(\mu_{1}\) | 0.331681981441542 | 0.141082164173265 | |
\(1/ \{ 1 + ( h^{-1}(2\pi) )^{4} \}\) | 0.096154317825982 | ||
\(\nu_{1}\) | 0.020235634105536 | 0.141082164173265 | |
\(1/ \{1 + ( h^{-1}(2\pi+ \pi/2) )^{4} \}\) | 0.019196682744858 | ||
2 | \(1/ \{1 + ( h^{-1}(4\pi- \pi/2) )^{4} \}\) | 0.001307826261601 | |
\(\mu_{2}\) | 0.001302361278230 | 0.002023744499666 | |
\(1/ \{ 1 + ( h^{-1}(4\pi) )^{4} \}\) | 0.000493666532259 | ||
\(\nu_{2}\) | 0.000221108040807 | 0.000262740095219 | |
\(1/ \{1 + ( h^{-1}(4\pi+ \pi/2) )^{4} \}\) | 0.000221067748587 | ||
3 | \(1/ \{1 + ( h^{-1}(6\pi- \pi/2) )^{4} \}\) | 0.000062476665124 | |
\(\mu_{3}\) | 0.000062476224272 | 0.000068406697161 | |
\(1/ \{ 1 + ( h^{-1}(6\pi) )^{4} \}\) | 0.000037391554101 | ||
\(\nu_{3}\) | 0.000023682280310 | 0.000025034538029 | |
\(1/ \{1 + ( h^{-1}(6\pi+ \pi/2) )^{4} \}\) | 0.000023682273941 | ||
4 | \(1/ \{1 + ( h^{-1}(8\pi- \pi/2) )^{4} \}\) | 0.000010806849662 | |
\(\mu_{4}\) | 0.000010806849551 | 0.000011218760557 | |
\(1/ \{ 1 + ( h^{-1}(8\pi) )^{4} \}\) | 0.000007675613651 | ||
\(\nu_{4}\) | 0.000005598484481 | 0.000005751016121 | |
\(1/ \{1 + ( h^{-1}(8\pi+ \pi/2) )^{4} \}\) | 0.000005598484479 | ||
5 | \(1/ \{1 + ( h^{-1}(10\pi- \pi/2) )^{4} \}\) | 0.000003179547340 | |
\(\mu_{5}\) | 0.000003179547340 | 0.000003244546827 | |
\(1/ \{ 1 + ( h^{-1}(10\pi) )^{4} \}\) | 0.000002462115765 | ||
\(\nu_{5}\) | 0.000001935846573 | 0.000001966635852 | |
\(1/ \{1 + ( h^{-1}(10\pi+ \pi/2) )^{4} \}\) | 0.000001935846573 |