Harmonic numbers associated with inversion numbers in terms of determinants | Zendy

Takao Komatsu | Zendy; Amalia Pizarro-Madariaga | Zendy

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Harmonic numbers associated with inversion numbers in terms of determinants

Author(s) -

Takao Komatsu,

Amalia Pizarro-Madariaga

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1809-52

Subject(s) - harmonic number , mathematics , bernoulli number , arithmetic function , inversion (geology) , euler's formula , real number , euler number (physics) , bernoulli's principle , pure mathematics , discrete mathematics , mathematical analysis , backward euler method , euler equations , riemann hypothesis , semi implicit euler method , paleontology , structural basin , biology , engineering , aerospace engineering

It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.

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