Generating function of the arithmetical function rd(n) and its relation to the Casimir energy

Details Generating function of the arithmetical function rd(n) and its relation to the Casimir energy Generating function of the arithmetical function rd(n) and its relation to the Casimir energy

2004-11-17

arxiv.org/abs/math-ph/0411056v1

Physics

Mathematical Physics

18 pages, 2 figures

Scientific paper

We obtain analytical expressions for the generating function $\xi_d(\lambda)$ of the sum of $d$-squares arithmetical function $r_d(n)$ where $\lambda$ is a free parameter. The original $d$-dimensional infinite sum is reduced to a formula containing a single finite sum over a convergent series. We compare the formulas to numerical computations and show that the percentage difference is negligible at small $\lambda$ for various values of $d$. $\xi_d(\lambda)$ divides naturally into two terms and we show that one term has a direct physical application to the $d$-dimensional Casimir energy of massless scalar fields in cubic cavities.

Affiliated with

Also associated with

No associations

Rating

Generating function of the arithmetical function rd(n) and its relation to the Casimir energy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generating function of the arithmetical function rd(n) and its relation to the Casimir energy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generating function of the arithmetical function rd(n) and its relation to the Casimir energy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-655346