On another note concerning integration:
Could the function \( ^xa \) be defined as some integral \( \int^{x_2}_{x_1}f(a,x,t)dt \)? The Gamma function and the Beta function, both extending some function on the integers (factorial and binomial coefficients, respectively), are defined in such a way, so it stands to reason there might be a similar integral for tetration.
Could the function \( ^xa \) be defined as some integral \( \int^{x_2}_{x_1}f(a,x,t)dt \)? The Gamma function and the Beta function, both extending some function on the integers (factorial and binomial coefficients, respectively), are defined in such a way, so it stands to reason there might be a similar integral for tetration.
