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Mar
20
revised Suplement books for calculus course?
added 131 characters in body
Mar
16
comment Help on Apostol's explanation of Archimedes method?
@neuguy For example, why start with $(k+1)^3$? I'm not really sure of what is happening in there, then I asked it vaguely: I was hoping that someone could rephrase it adding a little bit more detail perhaps?
Mar
16
asked Help on Apostol's explanation of Archimedes method?
Mar
16
revised Suplement books for calculus course?
added 74 characters in body
Mar
15
asked Suplement books for calculus course?
Feb
27
awarded  Yearling
Feb
23
comment How to solve this distribution problem with generating functions?
@Taussig Sorry,I meant 3 boxes. I forgot to add it.
Feb
23
revised How to solve this distribution problem with generating functions?
added 4 characters in body
Feb
23
asked How to solve this distribution problem with generating functions?
Feb
19
comment Is it possible to represent any sequence as the coefficients of arbitrary generating functions?
@whacka What's the meaning of sufficiently radical? I googled it and most of the results are about radical christianism(?!) and suffixing "math", yields something that also seems completely unrelated.
Feb
18
comment Is it possible to represent any sequence as the coefficients of arbitrary generating functions?
@whacka Got it. I got curious on a generating function which can't be expressed in a nice closed-form. Could you give me an example?
Feb
18
comment Is it possible to represent any sequence as the coefficients of arbitrary generating functions?
@whacka The problem is here: "you can form a corresponding generating function". I've looked (in my lectures) at few methods for finding generating functions. They are basically the expansion $(1-x)^n$ and $\left[ \frac{1}{1-x} \right]^n$, derivating and integrating one series and performing the sum/multiplication of two series. With this, it's not really clear that every sequence could be produced in the coefficients of the generating function.
Feb
17
comment On the calculus of recurrence relations using generating functions?
Oh, I got it. I was being stupid of not checking it by expanding a few terms. I did it now and I noticed they are the same. $$a_0+\sum_{k\ge 1}(ba_{k-1}x^k+cx^k)=a_0+(ba_0x^1+cx^1+\cdots)+(ba_1x^2+cx^2+\dots)$$ $$a_0+bx\sum_{k\ge 0}a_kx^k+cx\sum_{k\ge 0}x^k=a_0+(ba_0x^1+ba_1x^2+\dots)+(cx^1+cx^2+ \dots ) $$
Feb
17
comment On the calculus of recurrence relations using generating functions?
I guess this part is not clear: $$a_0+\sum_{k\ge 1}(ba_{k-1}x^k+cx^k)=a_0+bx\sum_{k\ge 0}a_kx^k+cx\sum_{k\ge 0}x^k$$ Do we push the $bx,cx$ outside the summation because they have already been processed by $\sum_{k\geq 1}$? I guess this make sense because the next summations start from $k\geq 0$.
Feb
17
asked On the calculus of recurrence relations using generating functions?
Feb
17
comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears?
Is it a general idea that I can leave the higher powers to simplify it? Aren't there ocasions when such procedure fails?
Feb
17
comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears?
Why only the coefficient of $x^{11}$? Don't you need to count the coefficients of $x^{11},x^{10},x^{9}$? There is (for example) the ocasion when each kid has $3$ oranges, no?
Feb
17
comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears?
@N.F.Taussig Yes.
Feb
16
comment In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears?
@Uncountable Yes, it was a typo. Thanks.
Feb
16
asked In how many ways can we distribute $11$ oranges and $6$ pears to $3$ kids, such that each kid gets at least $3$ orange and a maximum of $2$ pears?