12/23/2010, 01:29 PM
your question is not totally clear to me.
but afaik it is not known how everything can be put into a product.
for instance , i dont know an infinite product form that gives zeta(s) for all real parts with 1/2 < re(s) and NOT for re(s) < 1/2.
id love to see that.
a function can be analytically continued if it doesnt have a natural boundary , more specifically until it reaches a natural boundary.
and that is true independant of how the function is computed ( product , sum , integral , limit ) because the analytic computation form is another computation indepenent of how the original function was defined. ( since analytic continuation is unique ! )
hope i expressed myself clearly.
regards
tommy1729
but afaik it is not known how everything can be put into a product.
for instance , i dont know an infinite product form that gives zeta(s) for all real parts with 1/2 < re(s) and NOT for re(s) < 1/2.
id love to see that.
a function can be analytically continued if it doesnt have a natural boundary , more specifically until it reaches a natural boundary.
and that is true independant of how the function is computed ( product , sum , integral , limit ) because the analytic computation form is another computation indepenent of how the original function was defined. ( since analytic continuation is unique ! )
hope i expressed myself clearly.
regards
tommy1729
