How about re-writing with Cauchy Residue formula?
$$ \alpha_n(x) = \frac{(2n+1)!}{2\pi i} \oint \frac{dz}{(z-x)^{2n+2}}\cdot frac{dz}{z^{2n+2}}\cdot \frac{\sinh z }{\cosh z -1 + x} $$
Not sure how it helps you find roots or establish they are real.
|
2 | formula was incorrect | ||
|
|
||||
|
|
1 |
|
||
|
How about re-writing with Cauchy Residue formula? $$ \alpha_n(x) = \frac{(2n+1)!}{2\pi i} \oint \frac{dz}{(z-x)^{2n+2}}\cdot \frac{\sinh z }{\cosh z -1 + x} $$ Not sure how it helps you find roots or establish they are real. |
||||
