Corrigendum to “An Extension of Sheffer Polynomials”

(Proyecciones Journal of Mathematics*,* Vol*.* 30*,* No 2*,* pp*.* 265 *-* 275)

We regret to announce that there are some mathematical errors in theorem 2.3 and theorem 2.4. Our aim to correct and modify the theorem 2.3 and theorem 2.4.

Brown (^{1}) stated that {*B*
_{n}(*x*)} is a polynomial sequence which is simple and of degree precisely n. {*B*
_{n}(*x*)} is a binomial sequence if

and a simple polynomial sequence {_{
Pn
} (*x*)} is a Sheffer sequence if there is a binomial sequence {*B*
_{n}(*x*)} such that

**Theorem 2.3:** Let _{
pn
} (*x,y*) be symmetric, a class of polynomials in two variables and Sheffer A-type zero which belong to the operator *J(D)* and have the generating function as equation (1.11) of theorem 2.1 (See (^{2})). There exist sequences
and *η*
_{k}, independent of *x, y* and *n*, such that for all *n* ≥ 1,

where μ_{k} = (*k* + 1)*g*
_{k} in terms of *g*
_{k} of equation (1.8) and *η*
_{k} = (*k* + 1) *h*
_{k}, in terms of *h*
_{k} of equation (1.9).

Proof: Let (See (^{(2)}))

Thus we get

This gives the proof of statement.

**Theorem 2.4:** A necessary and sufficient condition that _{
pn
} (*x,y*) be of Sheffer A-type zero, there exists sequence _{
gk
} and _{
hk
} , independent of *x,y* and *n*, such that

Where _{
pn
} (*x,y*) is symmetric and a class of polynomials in two variables.

**Proof:** Let (See (^{(2)})

Thus