Pseudo-factorials, elliptic functions, and continued fractions

Details Pseudo-factorials, elliptic functions, and continued fractions Pseudo-factorials, elliptic functions, and continued fractions

2009-01-12

arxiv.org/abs/0901.1379v2

Mathematics

Classical Analysis and ODEs

24 pages; with correction of typos and minor revision. To appear in The Ramanujan Journal

Scientific paper

This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials. These numbers are associated with special elliptic functions, most notably, a Dixonian and a Weierstrass function, which parametrize the Fermat cubic curve and are relative to a hexagonal lattice. A continued fraction expansion of the ordinary generating function of pseudo-factorials, first discovered empirically, is established here. This article also provides a characterization of the associated orthogonal polynomials, which appear to form a new family of "elliptic polynomials", as well as various other properties of pseudo-factorials, including a hexagonal lattice sum expression and elementary congruences.

Affiliated with

Also associated with

No associations

Rating

Pseudo-factorials, elliptic functions, and continued fractions 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 Pseudo-factorials, elliptic functions, and continued fractions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pseudo-factorials, elliptic functions, and continued fractions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-531887