Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number

Details Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number

2007-07-26

arxiv.org/abs/0707.3950v2

Mathematics

Classical Analysis and ODEs

sharp error estimates and general formulas for Ramanujan's harmonic number expansion; correction of typo in the Ramanujan-Lodg

Scientific paper

An algebraic transformation of the DeTemple-Wang half-integer approximation to the harmonic series produces the general formula and error estimate for the Ramanujan expansion for the nth harmonic number into negative powers of the nth triangular number. We also discuss the history of the Ramanujan expansion for the nth harmonic number as well as sharp estimates of its accuracy, with complete proofs, and we compare it with other approximative formulas.

Affiliated with

Also associated with

No associations

Rating

Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number 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 Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40927