and are given by
The ordinary Bessel polynomials are those found with , [a2].
The moments associated with the Bessel polynomials satisfy
and are given by .
The weight equation is
where is any function with moments. This equation has been solved when
Using the three-term recurrence relation
|[a1]||S.S. Kim, K.H. Kwon, S.S. Han, "Orthogonalizing weights of Tchebychev sets of polynomials" Bull. London Math. Soc. , 24 (1992) pp. 361–367|
|[a2]||H.L. Krall, O. Frink, "A new class of orthogonal polynomials: The Bessel polynomials" Trans. Amer. Math. Soc. , 63 (1949) pp. 100–115|
|[a3]||P. Maroni, "An integral representation for the Bessel form" J. Comp. Appl. Math. , 57 (1995) pp. 251–260|
Bessel polynomials. A.M. Krall (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bessel_polynomials&oldid=11258