Relations Established Between Hypergeometric Functions and Some Special Number Sequences

In this study, we establish novel hypergeometric representations for the two classical sequences that are the Pell and Jacobsthal sequences. Building on Dilcher’s hypergeometric formulation of the Fibonacci sequence, we extend similar results and derive analogous structures for these two classical sequences. The results unify several known identities, provide new explicit representations, and offer a broader perspective on hypergeometric interpretations of linear second order recurrence sequences.