Convolution identities involving the central binomial coefficients and Catalan numbers

نویسندگان
Kucuk, Hakan ID 1
Sorgun, Sezer ID 2
Batır, Necdet ID 3

1 Department of Mathematics, Nev¸ sehir Hacı Bekta¸ s Veli University, 50300, Nev¸ sehir, Turkey

2 Department of Mathematics, Nev¸ sehir Hacı Bekta¸ s Veli University, 50300, Nev¸ sehir, Turkey

3 Department of Mathematics, Nev¸ sehir Hacı Bekta¸ s Veli University, 50300, Nev¸ sehir, Turkey

doi
10.22108/toc.2021.127505.1821
چکیده

We generalize some convolution identities due to Witula and Qi et al‎. ‎involving the central binomial coefficients and Catalan numbers‎. ‎Our formula allows us to establish many new identities involving these important quantities‎, ‎and recovers some known identities in the literature‎. ‎Also‎, ‎we give new proofs of Shapiro's Catalan convolution and a famous identity of Haj\'{o}s‎.

کلیدواژه‌ها
‎Convolution Identity‎, ‎Combinatorial Identity‎, ‎Central Binomial Coefficient‎, ‎Catalan Number‎, ‎Harmonic Number