AlanH
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 Apr11 comment Solving functional equation for generating function But doesn't that change the value of the sum? Apr11 comment Solving functional equation for generating function Yeah, I've been trying to figure out how to get the indices to start at $0$ all day. Why is it you can just start the the indices (in your hint) at $0$? Apr11 comment Simplifying Catalan number recurrence relation @BrianM.Scott In the first half of your answer, how do you go from $1+x\sum_{n\ge 0}\sum_{k=0}^nC_kC_{n-k}x^n$ to $1+x\left(\sum_{n\ge 0}C_nx^n\right)^2$ Apr10 comment Finding functional equation for generating function yeah, it's not a big deal. :) I was just sort of stating it as an fyi. Apr10 comment Finding functional equation for generating function your solution doesn't match the solution in the text :[ Apr9 comment Functional equations and generating functions oh wow...Thanks for that. Apr9 comment Functional equations and generating functions okay so you used the generalized binomial theorem, then how do you get the coefficient of $x^k$ in (3)? Apr9 comment Functional equations and generating functions @robjohn I was curious what rollback was. I'll change it back; I didn't edits bumped questions up. Sorry. I'm still going through your response. Apr3 comment Recurrence relation for number of different square subboards I see that, but I don't see how my text arrived at $a_n = a_{n-1} + 2\binom{n}{2} + n$ and $a_n = 2\binom{n+1}{3} + \binom{n+1}{2}$ Apr3 comment Stupid question - How do I calculate $\Phi(1.5)$? Use a z-table... Mar30 comment Discretization of Inhomogeneous Dirichlet Boundary Conditions for 2D Poisson's Equations I updated my solution! Mar29 comment Definition of a covering and how it applies to the following example @ChrisEagle Does that better clarify it? Mar27 comment Nasty Integral - Closed form solution? @okj where did you get this integral? Mar26 comment Recurrence relation for the number of $n$-digit ternary sequences with no consecutive $1$s or $2$s When you did the induction hypothesis, did you obtain that from the solution or did you deduce that from the closed form? (Very helpful solution, ow!) Mar25 comment Finding the remainder could the first method always be applied in cases of synthetic division? Mar24 comment Question about generating functions WHOA! How do you do the mouse-over effect?! Mar24 comment how to prove $\sum _{|k|\lt\sqrt m}\binom{2m}{m+k}\ge2^{2m-1}$ how did you go from the second line to the third line? Mar23 comment Why does Möbius transformation $f(z)$ map the unit disk $|z|<1$ to itself? Please see if the edit was what you intended for. Mar22 comment Recurrence relation for the number of ternary trings containing 2 consecutive zeros vs not containing If you don't mind, could you clarify or, rather, elaborate on your explanation after the equalities? Mar22 comment Recurrence relation for the number of ternary trings containing 2 consecutive zeros vs not containing How do you obtain the closed form without OEIS?