Finding the values of the coefficients from the following two equations.

Finding the values of the coefficients from the following two equations.

We have these following two equations,

where,

and

We need to calculate the terms ($A_1,A_2, B_1$ and $B_2$) so that for
example, $p_1(R)$ and $A_1 p_1(q) + B_1 p_2(q)$ represent the same
function; we could do this by requiring that, at some point $R_0$, both
sides of this equation have the same value and the same derivative.