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On the harmonic continued fractions

Journal Article


Abstract


  • In this paper, we study the harmonic continued fractions. These form an infinite family of ordinary continued fractions with coefficients t1,t2,t3,… for all t> 0. We derive explicit formulas for the numerator and the denominator of the convergents. In particular, when t is an even positive integer, we derive the limit value of the harmonic continued fraction. En route, we define and study convolution alternating power sums and prove some identities involving Euler polynomials and Stirling numbers, which are of independent interest.

Publication Date


  • 2019

Citation


  • Bunder, M., Nickolas, P. & Tonien, J. (2019). On the harmonic continued fractions. The Ramanujan Journal, 49 (3), 669-697.

Scopus Eid


  • 2-s2.0-85062478160

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/2703

Number Of Pages


  • 28

Start Page


  • 669

End Page


  • 697

Volume


  • 49

Issue


  • 3

Place Of Publication


  • United States

Abstract


  • In this paper, we study the harmonic continued fractions. These form an infinite family of ordinary continued fractions with coefficients t1,t2,t3,… for all t> 0. We derive explicit formulas for the numerator and the denominator of the convergents. In particular, when t is an even positive integer, we derive the limit value of the harmonic continued fraction. En route, we define and study convolution alternating power sums and prove some identities involving Euler polynomials and Stirling numbers, which are of independent interest.

Publication Date


  • 2019

Citation


  • Bunder, M., Nickolas, P. & Tonien, J. (2019). On the harmonic continued fractions. The Ramanujan Journal, 49 (3), 669-697.

Scopus Eid


  • 2-s2.0-85062478160

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/2703

Number Of Pages


  • 28

Start Page


  • 669

End Page


  • 697

Volume


  • 49

Issue


  • 3

Place Of Publication


  • United States