Some infinite representations of functions

wow, these are like series but epic. Do they converge to a value?

stanistanialandian↗

wow, these are like series but epic. Do they converge to a value?

They all have their own radii of convergence like infinite sums do. I recall at this moment that for the arctangent expression its for y less than or equal to pi/2, but i’m not sure for the other ones.

I know we use Lambert w function for solving x if both base and exponent are x but what do we use cube roots for?

XxkingxX↗

I know we use Lambert w function for solving x if both base and exponent are x but what do we use cube roots for?

solving cubic equations