Heidar
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 Aug14 awarded Nice Question Mar5 awarded Popular Question May24 awarded Commentator May24 comment A “simple” 3rd grade problem…or is it? Well, it depends on the topology of the board. The teacher is right if the board has the topology of, say, a ring or a torus. ;) Nov7 awarded Enthusiast Apr2 accepted “Non-commutative” Recurrence relation $C_m = \alpha_m C_{m-1} + \beta_m C_{m-2}$ Mar26 revised Construction of polynomials with non-commutative elements. edited title Mar26 revised Construction of polynomials with non-commutative elements. Explanation added Mar26 comment Construction of polynomials with non-commutative elements. @Mark, If you follow the link in my comment above you will see that this is the exact recursion relation I am trying to solve. I will edit my question and make it more clear what I am trying to achieve. Mar26 revised Construction of polynomials with non-commutative elements. added 18 characters in body Mar26 comment Construction of polynomials with non-commutative elements. It's part of a calculations I am doing regarding correlation functions in AdS/CFT correspondence around a rotating black hole background, more concretely I am working with many coupled PDE's. Even more concretely, I'm trying to find a solution for the recurrence relation in my last question (math.stackexchange.com/questions/123477/…). Mar26 asked Construction of polynomials with non-commutative elements. Mar26 comment “Non-commutative” Recurrence relation $C_m = \alpha_m C_{m-1} + \beta_m C_{m-2}$ Thanks for your suggestion Henry, I am afraid that this expression is slightly too abstract for my needs. It would be nicer to have $P_m(\alpha,\beta)$ written in terms of concrete sums and products. By the way, your expression doesn't seem to take into account that none of the $\alpha$ and $\beta$'s commute. Mar23 revised “Non-commutative” Recurrence relation $C_m = \alpha_m C_{m-1} + \beta_m C_{m-2}$ deleted 70 characters in body; edited title Mar22 revised “Non-commutative” Recurrence relation $C_m = \alpha_m C_{m-1} + \beta_m C_{m-2}$ deleted 11 characters in body Mar22 asked “Non-commutative” Recurrence relation $C_m = \alpha_m C_{m-1} + \beta_m C_{m-2}$ Nov7 awarded Scholar Nov7 accepted Contour Integration and Branch Cuts Nov7 comment Contour Integration and Branch Cuts Yeah, I need to look into it. There are just many integrals of the same type in this field and all of them gives hypergeometric functions (this can we shown to be the correct solution by other independent methods). I think the conclusion is that I'm misunderstanding some details in what these papers do. I am now pretty convinced that the way I understood the integrals to begin with, cannot be correct. Thanks for your nice answer, it has been very helpful. Nov7 awarded Editor