On q -congruences related to Hn(x;q) and Mn(x;q)
Indian Journal of Pure and Applied Mathematics, cilt.56, sa.2, ss.778-790, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 56 Sayı: 2
- Basım Tarihi: 2025
- Doi Numarası: 10.1007/s13226-023-00520-0
- Dergi Adı: Indian Journal of Pure and Applied Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
- Sayfa Sayıları: ss.778-790
- Anahtar Kelimeler: Congruence, Harmonic number, q-analog number
- Kocaeli Üniversitesi Adresli: Evet
Özet
In this paper, we examine ∑k=mp-1qk[km]qHk(x;q)(mod[p]q) and Mp-1(x;q)(mod[p]q), where for real number x, Hn(x;q)=∑k=1nxk[k]q and Mn(x;q)=∑k=1nkxk[k]q. For example, for an odd prime number p and m∈ { 0 , 1 ,.. , p- 2 } , [m+1]q∑k=mp-1qk[km]qHk(x;q)≡(-1)mq-(m2)(1-(x;q)p)-qm(xq;q)mxm+1[p]x(mod[p]q).