Open AccessEuler sums of generalized harmonic numbers and connected extensions
Author(s) -
Mümün Can,
Levent Kargın,
Ayhan Dil,
Gültekin Soylu
Publication year - 2023
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm210122014c
Subject(s) - harmonic number , mathematics , euler's formula , proof of the euler product formula for the riemann zeta function , binomial coefficient , euler number (physics) , riemann hypothesis , reciprocal , harmonic , series (stratigraphy) , euler summation , binomial (polynomial) , riemann zeta function , pure mathematics , mathematical analysis , combinatorics , semi implicit euler method , backward euler method , arithmetic zeta function , euler equations , prime zeta function , quantum mechanics , paleontology , linguistics , philosophy , physics , statistics , biology
This paper presents the evaluation of the Euler sums of generalized hyperharmonic numbers H(p,q)n ?H(p,q)(r) = ?Xn=1 H(p,q)n/nr in terms of the famous Euler sums of generalized harmonic numbers. Moreover, several infinite series, whose terms consist of certain harmonic numbers and reciprocal binomial coefficients, are evaluated in terms of the Riemann zeta values.