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Impossible functions ?

by zetafunction
Tags: functions, impossible
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zetafunction
#1
Apr17-09, 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} (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'
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