Theory and Modern Applications
Table 2 Certain members belonging to the Boas–Buck family
From: Certain results on a hybrid class of the Boas–Buck polynomials
S. No. | C(t) and B(t) | Polynomial set | Generating function |
|---|---|---|---|
I | C(t)=t | Brenke polynomials [17] | \(A(t)B(xt)=\sum_{n=0}^{\infty }Y_{n}(x)\frac{t^{n}}{n!}\) |
II | B(t)=exp(t) | Sheffer polynomials [18] | \(A(t)\exp (xC(t))=\sum_{n=0}^{\infty }S_{n}(x)\frac{t^{n}}{n!}\) |
III | C(t)=t & B(t)=exp(t) | Appell polynomials [19] | \(A(t)\exp (xt)=\sum_{n=0}^{\infty }L_{n}(x)\frac{t^{n}}{n!}\) |