Non-recursive in this context means functions that aren’t computationally equivalent to those computable by recursive functions only [1]. This is equivalent to

Non-recursive in this context means functions that aren’t computationally equivalent to those computable by recursive functions only [1]. This is equivalent to Turing completeness. It’s the second & third meaning in your link. A “non-recursive function” would be more powerful than that; or, conversely, it would be a function which cannot be computed using a Turing machine. Alternatively, these are also know as super-recursive functions [2]. [1] https://en.wikipedia.org/wiki/Computable_function https://en.wikipedia.org/wiki/Computable_function [2] https://en.wikipedia.org/wiki/Super-recursive_algorithm https://en.wikipedia.org/wiki/Super-recursive_algorithm