Bessel Polynomial
المؤلف:
Carlitz, L
المصدر:
"A Note on the Bessel Polynomials." Duke Math. J. 24
الجزء والصفحة:
...
15-9-2019
3603
Bessel Polynomial
Krall and Fink (1949) defined the Bessel polynomials as the function
where 
is a modified Bessel function of the second kind. They are very similar to the modified spherical bessel function of the second kind 
. The first few are
(OEIS A001497). These functions satisfy the differential equation
 |
(8)
|
Carlitz (1957) subsequently considered the related polynomials
 |
(9)
|
This polynomial forms an associated Sheffer sequence with
 |
(10)
|
This gives the generating function
 |
(11)
|
The explicit formula is
where 
is a double factorial and 
is a confluent hypergeometric function of the first kind. The first few polynomials are
(OEIS A104548).
The polynomials satisfy the recurrence formula
 |
(18)
|
REFERENCES:
Carlitz, L. "A Note on the Bessel Polynomials." Duke Math. J. 24, 151-162, 1957.
Grosswald, E. Bessel Polynomials. New York: Springer-Verlag, 1978.
Krall, H. L. and Fink, O. "A New Class of Orthogonal Polynomials: The Bessel Polynomials." Trans. Amer. Math. Soc. 65, 100-115, 1949.
Roman, S. "The Bessel Polynomials." §4.1.7 in The Umbral Calculus. New York: Academic Press, pp. 78-82, 1984.
Sloane, N. J. A. Sequences A001497, A001498, and A104548 in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في التفاضل و التكامل
اخر الاخبار
اخبار العتبة العباسية المقدسة
