\[\mathit{Ec}^{2m+1}_{\nu}\left(z_{1},k^{2}\right)\frac{w_{2}(K)+w_{2}(-K)}{w_{2%
}(0)}=-k^{2}\operatorname{sn}\left(z_{1},k\right)\int_{-K}^{K}\operatorname{sn%
}\left(z,k\right)\frac{\mathrm{d}\mathsf{P}_{\nu}\left(y\right)}{\mathrm{d}y}%
\mathit{Ec}^{2m+1}_{\nu}\left(z,k^{2}\right)\,\mathrm{d}z,\]