\[\alpha^{(1)}_{\nu,m}=\dfrac{1}{2\pi}\int_{0}^{2\pi}\sin t\operatorname{me}_{%
\nu}\left(t,h^{2}\right)\operatorname{me}_{-\nu-2m-1}\left(t,h^{2}\right)\,%
\mathrm{d}t=(-1)^{m+1}\dfrac{2\mathrm{i}}{\pi}\dfrac{\operatorname{me}_{\nu}'%
\left(0,h^{2}\right)\operatorname{me}_{-\nu-2m-1}\left(0,h^{2}\right)}{h%
\operatorname{D}_{1}\left(\nu,\nu+2m+1,0\right)}.\]