\[\alpha_{k}(\nu)=\frac{(4\nu^{2}-1^{2})(4\nu^{2}-3^{2})\cdots(4\nu^{2}-(2k+1)^{%
2})}{(k+1)!}\*\left(\frac{1}{4\nu^{2}-1^{2}}+\frac{1}{4\nu^{2}-3^{2}}+\cdots+%
\frac{1}{4\nu^{2}-(2k+1)^{2}}\right).\]