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Jun
5
comment Generating function for Banach's matchbox problem
Using this relation between $p_{k,m,n}$ and $p_{m,n}$, We don't need generating functions. I want to study generating functions more closely, so I posted this question.
Jun
5
answered Integral of $\int \frac{5x+1}{(2x+1)(x-1)}$
Jun
5
revised Generating function for Banach's matchbox problem
added 206 characters in body
Jun
5
comment Generating function for Banach's matchbox problem
Alright. I'm looking for anybody else interpreting the equation (2) directly, other wise I'll take your answer.
Jun
4
revised Generating function for Banach's matchbox problem
added 1 characters in body
Jun
4
asked Generating function for Banach's matchbox problem
Jun
4
suggested suggested edit on How to solve $x_j y_j = \sum_{i=1}^N x_i$
Jun
4
awarded  Citizen Patrol
Jun
4
comment Explicit formula for recurrence relation $a_{n+1} = 2a_n + 1$
Duplicated: math.stackexchange.com/q/106036/23875
Jun
4
comment The Fermat prime 257 and binomial sum $\sum_{n=0}^\infty \frac{(-1)^n}{\binom {8n}{4n}}$?
Could you figure out the reference for such formulas?
Jun
4
awarded  Benefactor
Jun
4
accepted How to solve this recurrence
Jun
4
comment How to solve this recurrence
The recurrence is related to Lemma 2 in Knuth's first analysis. Am I right?
Jun
4
comment How to solve this recurrence
Thanks. I will first read some of these articles.
Jun
4
comment How to solve this recurrence
Yeah, it's really linear probing. I don't know it's an open problem, but what about my recurrence? It seems that the recurrence can be solved.
Jun
3
revised How to solve this recurrence
added 93 characters in body
Jun
3
comment When can we plug an arbitrary number into an equation on formal power series
The case of rational functions are not too difficult. I'm afraid I'll manipulate a more complex one, for example, on $e^z$ or something else.
Jun
3
comment When can we plug an arbitrary number into an equation on formal power series
I'm still confused. I might know that $A(z)$, or your notation $A_m$, is really formal objects, for example, apples, where multiplying means a magic merge of two apples. The formula is true whenever the number of each kind of apple is same. My question is on substituting the apple with concrete number, e.g. $\omega$. $\omega$ is so lucky that some of elements in neighborhood converges. What about plugging $2\omega$ into $A_0 = A_1 + \cdots + A_m$?
Jun
1
revised How to solve this recurrence
added 1 characters in body
Jun
1
comment How to solve this recurrence
@leonbloy The bug of ambiguity between horse and house is fixed.