@DanielFischer I wanna ask, according to Ramanujan, if
$$f(x)=\sqrt{ab+(a+c)^2+b\sqrt{ab+(a+c)^2+(b+c)\sqrt{ab+(a+c)^2+(b+2c)\sqrt{ab+\cdots}}}}$$
then
$$f(x)=a+b+c$$
How does one prove this one?
Also this one, is it possible the following problem has a unique solution
$$x=\sqrt{i+\sqrt{i^2+\sqrt{i^3+\sqrt{i^4+\sqrt{i^5+\sqrt{i^6+\cdots}}}}}}$$
where $i=\sqrt{-1}$.
I have a grid of points
Example
x 80 82.5 85 87.5 90
y 5 0.5 1.6 1.7 1.7 2.3
2.5 1.6 1.7 1.8 2.1 2.7
0 2.4 2.3 2.6 3.0 3.8
and I want to be able to find any point for example point (81,...
how do i compute
$\int_0^{\infty} \frac{\sqrt{x}}{x^2+2x+5} dx$
with complex analysis?
I feel like im calculating the residue wrong and I cant get to the answer correctly.
I tried to branch cut the real $0 \rightarrow \infty$ but I feel like im doing it wrong. any help is appriciated.
What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts?
For instance, a function $f$:
$f^{-1}(x)$ can be an inverse and a preimage and sometimes even $\frac{1}{f(x)}$. $f^...
