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Impossible functions ? 
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#1
Apr1709, 04:53 PM

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 [tex] f(x)= \int_{\infty}^{\infty} (tx)^{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}(xy)^{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' 


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