18
votes
2answers
166 views
+500
Conjectural closed-form representations of sums, products or integrals
What are some examples of infinite sums, products or definite integrals that have conjectural closed form representations that were confirmed by numerical calculations up to whatever maximum precision ...
0
votes
1answer
66 views
List Table(s) of Series Here
I've been interested in series expansions of all types of mathematical functions. I was wondering if anyone has ever created a large list of all types of series. For example, Wolfram's Mathworld's ...
1
vote
0answers
57 views
A gratifying re-encounter with a piece of math that was out of my mind
A series of real numbers is said to be conditionally convergent if it is convergent but not absolutely convergent.
By rearranging the terms of a conditionally convergent series we can make the ...
4
votes
6answers
512 views
What is some infinite series expansion for 3/7?
What is some infinite series expansion for 3/7? and so on for these fraction with digit in base 10? I can't think of some useful thing at all. Please generalize some useful series expression for all ...
1
vote
2answers
85 views
What is the list of theorem that are able to find out a sequence is converge or not?
A sequence is called converge if for every next term of the sequence is getting closer to the limit of a number.
What is the list of theorem that are able to helping to find out a sequence is converge ...
3
votes
1answer
292 views
Uses of Divergent Series and their summation-values in mathematics?
When I was trying to find closed-form representations for odd zeta-values, I used
$$ \Gamma(z) = \frac{e^{-\gamma \cdot z}}{z} \prod_{n=1}^{\infty} \Big( 1 + \frac{z}{n} \Big)^{-1} e^{\frac{z}{n}} $$ ...
131
votes
17answers
8k views
Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$
As I have heard people did not trust Euler when he first discovered the formula
$$\zeta(2)=\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}.$$
However, Euler was Euler and he gave other proofs.
I ...
4
votes
2answers
122 views
What is an alternative formulation to a contour integral?
Suppose that a rational generating function is given representing the function
$f(x) = \sum_{i=0}^{2n}{c_i x^i}$ where $c_i \in \mathbb{N}$
The goal is to determine if the coefficient in the middle, ...
