>>12814253Another really cool result. It's nothing special about the logarithmic derivative per se. Shouldn't it also be applicable with the integrand being f'/f''? After all, if the function is once differentiable it's infinitely differentiable (my favorite complex analysis result), and the existence of the poles and zeroes is also encoded in the derivatives. The principle will always pick up information on the essential poles, but the true deepness comes from picking up the simple poles. But that directly follows from just using f in the denominator and not any higher order derivatives.
