Convolution identities involving the central binomial coefficients and Catalan numbers

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.

Keywords:

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