- #1
zetafunction
- 391
- 0
given a function g(x) so the integral [tex] \int_{-\infty}^{\infty}dx g(x) [/tex] exists
could we find a complex valued function f(z) and a closed curve C so
[tex] \int_{-\infty}^{\infty}dx g(x)= \oint _ {C} dz f(z) [/tex]
then if we can calculate the residues of f(z) we can compute the real valued integral of g(x)
is this possible for any well-behaved functions f and g(x) ??
could we find a complex valued function f(z) and a closed curve C so
[tex] \int_{-\infty}^{\infty}dx g(x)= \oint _ {C} dz f(z) [/tex]
then if we can calculate the residues of f(z) we can compute the real valued integral of g(x)
is this possible for any well-behaved functions f and g(x) ??