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On Some General Tornheim-Type Series.
- Source :
-
Mathematics (2227-7390) . Jun2024, Vol. 12 Issue 12, p1867. 18p. - Publication Year :
- 2024
-
Abstract
- In this paper, we solve the open problem posed by Kuba by expressing ∑ j , k ≥ 1 H k (u) H j (v) H j + k (w) j r k s (j + k) t as a linear combination of multiple zeta values. These sums include Tornheim's double series as a special case. Our approach is based on employing two distinct methods to evaluate the specific integral proposed by Yamamoto, which is associated with the two-poset Hasse diagram. We also provide a new evaluation formula for the general Mordell–Tornheim series and some similar types of double and triple series. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ZETA functions
*PROBLEM solving
*HYPERGEOMETRIC series
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 12
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 178195296
- Full Text :
- https://doi.org/10.3390/math12121867