# Impossible functions ?

1. Apr 17, 2009

### zetafunction

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

$$f(x)= \int_{-\infty}^{\infty} (t-x)^{m}$$ 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'

Last edited: Apr 17, 2009