Question Number 223821 by wewji12 last updated on 06/Aug/25
$$\underset{\nu\rightarrow\alpha} {\mathrm{lim}}\:\frac{{J}_{−\nu−\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right)+{e}^{\boldsymbol{{i}}\pi\nu} \centerdot{Y}_{\nu+\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right)}{{Y}_{−\nu−\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right)−{e}^{\boldsymbol{{i}}\pi\nu} \centerdot{J}_{\nu+\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right)}=?? \\ $$$$\alpha\in\mathbb{Z}\: \\ $$