# Impossible functions ?

by zetafunction
Tags: functions, impossible
 P: 399 it is only a mere curiosity of calculus and do not if has any application the idea is how can we define the apparently impossible functions $$f(x)= \int_{-\infty}^{\infty} (t-x)^{m}$$ for m a real number $$g(s) = \sum _{primes} p^{s+a}$$ s+a >0 $$f(x)= \int_{-\infty}^{\infty}dt exp(-axt)$$ a can be a real or complex number $$f(x)= \int_{0}^{\infty}dy x^{a}(x-y)^{b}$$ a and b are real numbers a,b >0 $$f(x)= \int_{-\infty}^{\infty} duexp(ixf(u)$$ but 'f' is a complex valued function even for real 'x' as you can see all of them make no sense for any x real or complex since we always would have the same answer $$f(x)= \infty$$ for every real or complex 'x'