Tagged Questions
12
votes
1answer
167 views
How do solve this integral $\int_{-1}^1\frac{1}{\sqrt{1-x^2}}\arctan\frac{11-6\,x}{4\,\sqrt{21}}\mathrm dx$?
I need to solve the to following integral:
$$\int_{-1}^1\frac{1}{\sqrt{1-x^2}}\arctan\frac{11-6\,x}{4\,\sqrt{21}}\mathrm dx.$$
I tried this integral in Mathematica, but it was not able to solve it. ...
11
votes
2answers
200 views
Closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$.
What is the closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$? We can use Fourier series of $e^{-bx}$ ($|x|<\pi$) to evaluate $\sum_{n=-\infty}^{\infty}\frac{1}{n^2+b^2}$. But this ...
-2
votes
1answer
116 views
Integral question: zeroes of the primitive.
Let $z$ be a complex number.
Let $f(z)$ be an elementary function but not a polynomial.
Let its integral $F(z)$ be impossible to express in elementary functions.
If we define $F(z)$ as $\int$ from $A$ ...
11
votes
3answers
517 views
closed form of $\sum \frac{1}{z^3 - n^3}$
I am currently trying to find a closed form expression for $\displaystyle f(z) = \sum_{n \in \mathbb{Z}} \frac{1}{z^3 - n^3}$, $z \in \mathbb{C}$. After a set of twists and turns, I have hit a wall.
...
