There are several instances where the functional form is shown as
$$\beta_0 + f_1(X_1) + f_2(X_2, X3) + \ldots + f_M(X_N),$$
and I believe it should be
$$\beta_0 + f_1(X_1) + f_2(X_2) + f_3( X_3) + \ldots + f_M(X_M),$$
or even this
$$\beta_0 + f_1(X_1) +\ldots + f_M(X_M)$$
is probably sufficient.