(b) *wth* Order Deformation Problem

The following equations are satisfied by the problem of the *wth* order.

$$\left[L\_f[f\_w(\eta) - \chi\_w f\_{w-1}(\eta)] = h\_f \, R\_w^f(\eta)\right] \tag{37}$$

$$L\_{\mathbb{X}}[\mathbb{g}\_w(\mathfrak{n}) - \chi\_w \mathbb{g}\_{w-1}(\mathfrak{n})] = h\_{\mathbb{X}} \, R\_w^{\mathbb{g}}(\mathfrak{n}) \,. \tag{38}$$

$$L\_{\Phi}[\Theta\_{\mathfrak{w}}(\mathfrak{q}) - \chi\_{\mathfrak{w}}\Theta\_{\mathfrak{w}-1}(\mathfrak{q})] = h\_{\Phi} \, R\_{\mathfrak{w}}^{\Theta}(\mathfrak{q}),\tag{39}$$

$$L\_{\Phi}[\phi\_w(\eta) - \chi\_w \phi\_{w-1}(\eta)] = h\_{\Phi} \, R\_w^{\Phi}(\eta). \tag{40}$$

where

$$\chi\_w = \begin{cases} \ 0 \text{, if } q \le 1 \\\ \ 1 \text{, if } q > 1 \end{cases}$$
