(For $~x~$ is real)
Wolfram alpha calculates this value to be approx $~1.83377265168...~$
But does anyone know of a method in which we could find an exact value for this?
Also, are there any other interesting properties of this number that is known?
This is for my own curiosity as during one of my maths lessons on series I pondered this question, too which my teacher couldn't answer. While i do believe that this value does have interesting properties which may be used in some fields of number theory, I myself cannot see an immediate application. However, this said, the methods that would be used to solve such a problem could be transferable to similar problems.
Edit: I refer to exact value meaning a value that uses one of the known and calculable mathematics constants (e.g., $\pi, e,$ Apéry's constant, ect.) or involving a function (such as sqrt ect.)