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  Volume 9, Issue 3, Article 89
Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number

    Authors: Mark B. Villarino,  
    Keywords: Inequalities for sums, series and integrals, Approximation to limiting values  
    Date Received: 27/07/07  
    Date Accepted: 20/07/08  
    Subject Codes:

26D15, 40A25.

    Editors: Sever S. Dragomir,  

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.

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