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

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dc.creatorVillarino, Mark B.
dc.date2007-07-26
dc.date2007-07-28
dc.date.accessioned2026-07-07T08:20:40Z
dc.date.available2026-07-07T08:20:40Z
dc.descriptionAn 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.
dc.descriptionsharp error estimates and general formulas for Ramanujan's harmonic number expansion; correction of typo in the Ramanujan-Lodge lower bound constant; thanks to Jonathan Post and Martin Fuller; fixed typo in the title
dc.identifierhttps://arxiv.org/abs/0707.3950
dc.identifierhttp://arxiv.org/abs/0707.3950
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135134
dc.subjectClassical Analysis and ODEs
dc.subjectGeneral Mathematics
dc.subject26D5x, 33B15
dc.titleRamanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number
dc.typetext

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