Checking Identities Is Computationally Intractable (NP-Hard), So Human Provers Will Be Always Needed

In order to find a general framework for different combinatorial identities and identities that involve special functions, Bernshtein introduced in [1] a notion of holonomic functions. Let us recall this definition (in formulating it, we will follow [10]). A discrete holonomic function f(n) of one variable is defined as a solution of a homogeneous, linear difference equation with polynomial coefficients (to define continuous holonomic functions, we must change “difference” to “differential”). A holonomic function of several continuous and/or discrete variables is defined as a solution of a “maximally overdetermined” system of homogeneous linear partial differential–difference equation with polynomial coefficients.