I will be writing about the zeta function and finding a general formula for .All you need is a bit of knowledge in Calculus and Trigonometry.
Now let's get started.Remember the Taylor series for ?
Now let's divide both sides by x.
The zeros of the sine function occur when , where k is an integer.
Now let's substitute
Nobody likes to deal with infinite products, but if we take the logarithm of a product, it becomes a sum!
Now if we differentiate both sides with respect to s (I will not go through the derivation of this, just bash with the chain rule a bit), we will get
Now we multiply both sides by and we get
To be continued in Part 2.