impossible functions ?? 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 [tex] f(x)= \int_{-\infty}^{\infty} (t-x)^{m} [/tex] for m a real number [tex] g(s) = \sum _{primes} p^{s+a} [/tex] s+a >0 [tex] f(x)= \int_{-\infty}^{\infty}dt exp(-axt) [/tex] a can be a real or complex number [tex] f(x)= \int_{0}^{\infty}dy x^{a}(x-y)^{b} [/tex] a and b are real numbers a,b >0 [tex] f(x)= \int_{-\infty}^{\infty} duexp(ixf(u) [/tex] 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 [tex] f(x)= \infty [/tex] for every real or complex 'x'