Question

Which of the following is false regarding Bessel polynomials?

(a) Krall and Fink (1949) defined the Bessel polynomials

(b) The polynomials satisfy the recurrence formula

(c) The solutions of homogeneous equations are closely related to Bessel polynomials

(d) Bessel polynomials are not an orthogonal sequence of polynomials

I had been asked this question in semester exam.

My question is from Homogeneous Linear PDE with Constant Coefficient topic in division Partial Differential Equations of Engineering Mathematics

Answer 1

Correct answer is (d) Bessel polynomials are not an orthogonal sequence of polynomials

The explanation: The Bessel polynomials are an orthogonal sequence of polynomials. The most accepted definition for these series was put forth by Krall and Frink (1948) as,

\(y_n (x)=∑_{k=0}^n\frac{(n+k)!}{(n-k)!k!} (\frac{x}{2})^k.\)