Table 1 The \(QB_{i}(x)\), \({QB}'_{i}(x)\), \({QB}''_{i}(x)\), and \({QB}'''_{i}(x)\)
From: An inverse boundary value problem for transverse vibrations of a bar
| Â | \(x_{i-3}\) | \(x_{i-2}\) | \(x_{i-1}\) | \(x_{i}\) | \(x_{i+1}\) | \(x_{i+2}\) | \(x_{i+3}\) |
|---|---|---|---|---|---|---|---|
\(QB_{i}(x)\) | 0 | 1 | 26 | 66 | 26 | 1 | 0 |
\(QB'_{i}(x)\) | 0 | \(\xi _{1}\) | 10 \(\xi _{1}\) | 0 | \(-10 \xi _{1}\) | \(-\xi _{1}\) | 0 |
\(QB_{i}^{\prime\prime}(x)\) | 0 | \(\xi _{2}\) | 2\(\xi _{2}\) | \(-6\xi _{2}\) | 2\(\xi _{2}\) | \(\xi _{2}\) | 0 |
\(QB^{\prime\prime\prime}_{i}(x)\) | 0 | \(\xi _{3}\) | \(-2\xi _{3}\) | 0 | 2\(\xi _{3}\) | \(-\xi _{3}\) | 0 |
\(QB^{iv}_{i}(x)\) | 0 | \(\xi _{4}\) | −2\(\xi _{4}\) | \(6\xi _{4}\) | −2\(\xi _{4}\) | \(\xi _{4}\) | 0 |