According to wolfram, A generalization of the confluent hypergeometric differential equation is given by;

$$y”+left(frac{2R}{x}+2F’+pfrac{H’}{H}-H’-frac{H”}{H’}right) y’+left(left(pfrac{H’}{H}-H’-frac{H”}{H’}right)left(frac{R}{x}+F’right)+frac{R(R-1)}{x^2}+frac{2R}{x}F’+F”+(F’)^2-frac{q}{H}(H’)^2 right)y=0$$

Which has the solutions $y_1=x^{-R} e^{-F} M(q,p,H)$ and $y_2=x^{-R} e^{-F} O(q,p,H)$, where $M(q,p,H)$ is the confluent hypergeometric function of the first kind and $O(q,p,H)$ is the confluent hypergeometric function of the second kind. Meanwhile, $R,F$ and $H$ are fucntions of $x$.

I tried to look on google for more details about this equation but i didn’t find anything, can anyone here please give me more references about this particular equation? Like how it was deriven, the relation between the parameters $p$ and $q$..etc.

Thank you guys a lot.

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