I encounter this series in an old book of infinite series. The series is as followed:
Judging from the series, it must be an even function. Is it possible to find the closed form function for this series. Also, instead of the power of 2 in coefficients, we may have them in n. Do we have a general formula to generate the functions for power of n?
I try to differentiate this series but it doesn't seem to produce anything fruitful.