I'm currently reading an article on terrestrial gravitational noise done by Peter Saulson. He approximates a sum (Eq.4) by an integral with a inner cutoff radius of lambda/4 (Eq.5).
I don't manage to find the same result myself.
I attached the equations from the article + my integral derivation (see attached images)
Does someone know how to obtain the same result as in the paper ?
Regards,
QCP
Equations from the article:

Self derived integral:
