Evaluation formulas for the Tornheim and Euler-type double series
Hacettepe Journal of Mathematics and Statistics, cilt.53, sa.4, ss.926-941, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 53 Sayı: 4
- Basım Tarihi: 2024
- Doi Numarası: 10.15672/hujms.1165578
- Dergi Adı: Hacettepe Journal of Mathematics and Statistics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.926-941
- Anahtar Kelimeler: Bernoulli polynomial, Euler sum, Fourier series, Tornheim series, zeta function
- Akdeniz Üniversitesi Adresli: Evet
Özet
We give closed-form evaluation formulas for the real and imaginary parts of the series ∑∞m,n=1 e2πi(mx−ny) mpnr q (mc+n), c ∈ N, in terms of certain zeta values. Particular choices of x and y lead to evaluation formulas for some Tornheim-type∑∞ 1 m,n=1 and Euler-type ∑∞m,n=1 1 np(mc+n)q double series and their alternating analogues. mpnr (mc+n)q.