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Recurrence Relations for Linear Euler Harmonic Sums
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DOI：10.36045/j.bbms.251124.png)
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Abstract
En 中文
Euler's pioneering work on linear and non-linear harmonic sums has continued to inspire extensive research, yielding many new results. This paper studies representations of linear harmonic Euler sums of both even and odd weight. This work establishes new identites linking sums with positive terms to alternating series, introduces two symmetry properties at half integer value, and extends known recurrence relations for linear harmonic Euler sums of even and odd weight.
Keywords:
Harmonic number
linear harmonic Euler sums
extended harmonic number
parametric harmonic number
nonlinear harmonic Euler sums
parametric linear har-monic Euler sums
Riemann zeta function
Dirichlet eta function
generalized zeta function
psi function
polygamma function
polylogarithm function
Journal
B
IF:
0.6
Papers:
21
Citations:
0
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