Hello and thank you for trying to help.
In spite of the fact that this seems a very simple problem, I do not find myself able to get a solution. Here it goes:
Let $$f(x)=\displaystyle \sum_{k=3}^\infty a_k \frac{x^k}{k(k-1)(k-2)}$$ and $$g(x)=\displaystyle \sum_{k=0}^\infty a_k x^k$$. Express...
Is there a closed form for the constant given by:
$$\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(2))}{n}$$
(Where Ei is the exponential integral)?
Could we generalize it for:
$$I(k)=\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(k))}{n}$$
?
My try: As it is given that k will be a positive integer, I have...
Breaking it in 4 fractions would definitively lead to a sum of divergent integrals, but dividing it into 2 integrals:
x \displaystyle \int_2^\infty \frac{1}{y(y^2-1)\log(x+y)} + \int_2^\infty \frac{1}{(y^2-1)\log(x+y)}
Since the value of the second one is too small for large x, any idea...
Hello.
I am having a lot of trouble trying to solve/analyse this integral:
$$\displaystyle \int_2^\infty \frac{x+y}{(y)(y^2-1)(\ln(x+y))} dy$$
I have tried everything with no result; it seems impossible for me to work with that natural logarithn.
I have also tried to compute it, as it...