Hypergeometric connotations of quantum equations

We show that the Schrödinger and Klein–Gordon equations can both be derived from a hypergeometric differential equation. The same applies to non linear generalizations of these equations. •We show that both the Schrödinger and Klein–Gordon equations can be derived from the confluent hypergeometric differential equation.•Also a non linear Klein–Gordon equation can be analogously derived.•The latter coincides with one advanced by Nobre, Rego-Monteiro, and Tsallis.