Page 185 - Determinants and Their Applications in Mathematical Physics

5

Further Determinant Theory

5.1 Determinants Which Represent Particular
Polynomials

5.1.1 Appell Polynomial

Notes on Appell polynomials are given in Appendix A.4.
Let

n
n
ψ n (x)=(−1) n α n−r (−x) . (5.1.1)
r
r
r=0
Theorem.

α 0 α 1 α 2 α 3 ··· α n−1 α n

n
1 x x 2 x 3 ··· ··· x n

0

1 2x 3x ··· ··· x
2 n n−1
1
,
a. ψ n (x)=

n

1 3x ··· ··· x n−2

2

··· ··· ··· ···

1 nx

n+1