Several formulas and identities related to the Pochhammer k-symbol and application to a case of the Fuss–Catalan–Qi numbers

We give some formulas and series identities involving the Pochhammer k-symbol. In particular, we give generalizations of formulas and identities about the Catalan numbers and the Catalan–Qi numbers given in [F. Qi and B.-N. Guo, Integral representations of the Catalan numbers and their applications, Mathematics 5 (2017), no. 3, Article 40, available online at https://doi.org/10.3390/math5030040.] and [W. Chammam, Several formulas and identities related to Catalan–Qi and q-Catalan–Qi numbers, Indian J. Pure Appl Math., 50, (2019), 1039–1048; Available online at https://doi.org/10.1007/s13226-019-0372-1].