I found this question that was closed because it was unclear, yet it was a nice idea. I'll do my best to make this into a clear challenge.
The Riemann Zeta function is a special function that is defined as the analytical continuation of
to the complex plane. There are many equivalent formulas for it which makes it interesting for code golf.
Write a program that takes 2 floats as input (the real and imaginary part of a complex number) and evaluates the Riemann Zeta function at that point.
- Input and output via console OR function input and return value
- Built in complex numbers are not allowed, use floats (number, double, ...)
- No mathematical functions except
+ - * / pow logand real valued trig functions (if you want to integrate, use the gamma function, ... you must include this functions definition in the code)
- Input: 2 floats
- Output: 2 floats
- Your code must contain value that gives theoretically arbitrary precision when made arbitrary large/small
- The behaviour at input 1 is not important (this is the only pole of this function)
Shortest code in bytes wins!
Example Input and Output