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location Antarctica
age 79
visits member for 2 years, 2 months
seen Dec 16 at 5:42

Self-learning mathematics. Many thanks to those who make time to help others on the site.


Apr
11
comment Solving functional equation for generating function
But doesn't that change the value of the sum?
Apr
11
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 $0$?
Apr
11
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 $1+x\left(\sum_{n\ge 0}C_nx^n\right)^2$
Apr
10
comment Finding functional equation for generating function
yeah, it's not a big deal. :) I was just sort of stating it as an fyi.
Apr
10
comment Finding functional equation for generating function
your solution doesn't match the solution in the text :[
Apr
9
comment Functional equations and generating functions
oh wow...Thanks for that.
Apr
9
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)?
Apr
9
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.
Apr
3
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 $a_n = 2\binom{n+1}{3} + \binom{n+1}{2}$
Apr
3
comment Stupid question - How do I calculate $\Phi(1.5)$?
Use a z-table...
Mar
30
comment Discretization of Inhomogeneous Dirichlet Boundary Conditions for 2D Poisson's Equations
I updated my solution!
Mar
29
comment Definition of a covering and how it applies to the following example
@ChrisEagle Does that better clarify it?
Mar
27
comment Nasty Integral - Closed form solution?
@okj where did you get this integral?
Mar
26
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!)
Mar
25
comment Finding the remainder
could the first method always be applied in cases of synthetic division?
Mar
24
comment Question about generating functions
WHOA! How do you do the mouse-over effect?!
Mar
24
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?
Mar
23
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.
Mar
22
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?
Mar
22
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?