- #1
mhill
- 180
- 1
given the series
[tex]g(x)= \sum_{n=0}^{\infty}\frac{a_{n}}{\sqrt {x-n}}[/tex]
where the coefficients a_n are real numbers my question is does the above makes sense ? i mean since we are summing over all positive integers , no matter how big we choose 'x' there will be a factor so x-n n=0,1,2,3,4,..... (x-n) <0 then g(x) is complex no matter what real x we put.
If we approximate the series by an integral [tex]\int_{0}^{\infty}dr a(r) (x-r)^{-1/2}[/tex] we get a similar result, i do not know if this is paradoxical and i should have taken the absolute value |x| inside the square root.
[tex]g(x)= \sum_{n=0}^{\infty}\frac{a_{n}}{\sqrt {x-n}}[/tex]
where the coefficients a_n are real numbers my question is does the above makes sense ? i mean since we are summing over all positive integers , no matter how big we choose 'x' there will be a factor so x-n n=0,1,2,3,4,..... (x-n) <0 then g(x) is complex no matter what real x we put.
If we approximate the series by an integral [tex]\int_{0}^{\infty}dr a(r) (x-r)^{-1/2}[/tex] we get a similar result, i do not know if this is paradoxical and i should have taken the absolute value |x| inside the square root.