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Question impossible functions ( Physics Forums Calculus Analysis )
Updated: 2010-07-25 06:55:04 (0)
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

LaTeX Code:  f(x)= \\int_{-\\infty}^{\\infty} (t-x)^{m}  for m a real number

LaTeX Code:  g(s) = \\sum _{primes} p^{s+a}  s+a >0

LaTeX Code:  f(x)= \\int_{-\\infty}^{\\infty}dt exp(-axt)  a can be a real or complex number

LaTeX Code:  f(x)= \\int_{0}^{\\infty}dy x^{a}(x-y)^{b}  a and b are real numbers a,b >0

LaTeX Code:  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 LaTeX Code:  f(x)= \\infty  for every real or complex 'x'

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