# Questions tagged [ramanujan]

The tag has no usage guidance.

59 questions
Filter by
Sorted by
Tagged with
102 views

### How to find the right path of integration to get the asymptotic partition formula

I am trying to understand how the asymptotic partition formula $p(n) \sim \frac{e^{\pi\sqrt{\frac{2n}{3}}}}{4n\sqrt3}$ was derived for a project and have been reading and following many papers. I am ...
277 views

### Citation for the ill-posed Ramanujan's problem

I've seen many times the following problem posed by Ramanujan: $$\sqrt{1+2{\sqrt{1+3{\sqrt{1+\cdots}}}}} = \mbox{?}$$ This problem is also mentioned on Ramanujan's Wikipedia page along with the ...
197 views

534 views

### Statement of classical Ramanujan-Petersson conjecture

I'm preparing for an expository talk on some topics in the representation theory of reductive p-adic groups, including tempered representations and Whittaker models, and as motivation I wanted to ...
152 views

823 views

### What is the roadblock in the discovery of new taxicab numbers?

The $n$-th taxicab number, denoted $\text{Ta}(n)$, is the smallest integer that can be expressed as a sum of two positive integer cubes in $n$ different distinct ways. $\text{Ta}(1) = 2 = 1^3 + 1^3$ ...
732 views

### Two curious series for $1/\pi$

On Jan. 18, 2012 I conjectured that for any prime $p>3$ we have $$R_p^2\equiv\frac1{10}\left(512\left(\frac{10}p\right)-27\left(\frac{-15}p\right)-475\right)\pmod p,$$ where $(\frac{\cdot}p)$ ...
1k views

### What were Ramanujan's standard tricks/approaches to solving problems?

While trying to formulate an answer to this question, I realized I really have no idea how Ramanujan came up with his formulas. Bruce Berndt has a number of great expository articles, e.g., this one, ...
134 views

### What is the collection of series that amount to $\gamma$ deduced by Ramanujan?

On p. 20 of an article by Borwein et al., it is stated that Ramanujan could generalize the following formula due to Glaisher $$\gamma = 2 - 2\log2 -2\sum_{n=3, \text{ odd}} \frac{\zeta(n)-1}{n(n+1)}$$...
267 views

### Closed Form for $\sum\limits_{n=-2a}^\infty(n+a){2a\choose-n}^4,~a\not\in\mathbb Z$
Do either $~S_4^+(a)~=~\displaystyle\sum_{n=0}^\infty(n+a){2a\choose n}^4~$ or $~S_4^-(a)~=~\displaystyle\sum_{n=-2a}^\infty(n+a){2a\choose-n}^4~$ possess a meaningful closed form expression1 in terms ...