Generalized Jacobsthal polynomials and special points for them

In this work we introduce a family of polynomials that satisfy the recurrence relations for Jacobsthal polynomials with generalized initial conditions by analogy to work of V.K. Gupta, Y.K. Panwar, and O. Sikhwal from 2012. Explicit closed form and the Binet formulas for the generalized Jacobsthal polynomials are presented. The generating function and other relations for them are also found. Special points for this family are analyzed and presented pictorially.