Assume the tridiagonal matrix $T$ in this form: $$ T = \begin{bmatrix} a & c & & & \\ b & a & c & & \\ & b & a & \ddots & \\ & & b & a & \\ & & & b & \\ \end{bmatrix} $$ we must show the eagen valus have form $$ a+2\sqrt{bc}\, \cos(k \pi/{(n+1)}) $$
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That is clearly not true. For example, if all the $\gamma_i$ are zero, the eigenvalues are $\alpha_i$ for $i=1,\ldots,n$. – Harald Hanche-Olsen Oct 02 '14 at 07:15
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Do we know anything about $\alpha_i$, $\beta_i$, and $\gamma_i$? – JimmyK4542 Oct 02 '14 at 07:15
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yes.$a=q$h^2$-1$ and $b =$1-ph/{2}$ and $c =$1+ph/{2}$ such that$ q<=0$ – user157745 Oct 02 '14 at 07:35
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Please don't ask the same question twice. I am voting to close this one, as the other (newer) one has some answers. – Harald Hanche-Olsen Oct 02 '14 at 16:14