Tagged Questions

0
votes
1answer
66 views

Computing functions from generating functions

I am new to generating functions but understand how to derive them from given discrete numeric functions. Is there a simple way to derive the discrete numeric function given a generating function. For ...
2
votes
1answer
83 views

Construct a generating function for the components of a sum

Let $j \in Z_+$. Set $$ a_j^{(1)}=a_j:=\sum_{i=0}^j\frac{(-1)^{j-i}}{i!6^i(2(j-i)+1)!} $$ and $a_j^{(l+1)}=\sum_{i=0}^ja_ia_{j-i}^{(l)}$. Find generating function $\sum_{j}a_jx^j$ so that allows to ...
1
vote
2answers
90 views

An injective map where each value is mapped to many others?

I want "something" ("something" because maybe it is not really a mathematical function, called F in the above image) that can describe what is shown on the image. A given value from a domain Xi can ...
0
votes
2answers
72 views

Searching for a suitable invertible function

I am searching for a monotonically increasing and invertible function in $2$ variables. I know several monotonically increasing functions. This is also true for invertible functions. But I am ...
4
votes
1answer
72 views

Generating Functions: how do I get my answers in terms of differential operators?

I'm reading and enjoying "generatingfunctionology". What a great fun book! But, I'm having some difficulty with the exercises. For example, take the series $a_n = n^2$ I'd like to find the Generating ...
1
vote
1answer
116 views

How to transform/expand a simple sum to prove equality of two sets?

I have the set $A=\left\{1+\displaystyle\sum_{i=1}^n (3-(-1)^i)\;\text{ where }\;n\in\mathbb{N}_0\right\}$ and I have to prove equality with $B=\{x\in\mathbb{N}\;\text{ where }\;2 \text{ and } 3 ...
4
votes
4answers
457 views

Is it possible to convert a polynomial into a recurrence relation? If so, how?

I have been trying to do this for quite a while, but generally speaking the partially relevant information I could find on the internet only dealt with the question: "How does on convert a recurrence ...