zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some open problems of generalised Bessel polynomials. (English) Zbl 0583.33007

Das verallgemeinerte Besselpolynom y n (x;a,b)= 2 F 0 (-n,n+a-1,(-x/b)) vom Grad n ist Polynomlösung der Differentialgleichung

x 2 y '' +(ax+b)y ' -n(n+a-1)y=0(-aN 0 ,-bN 0 )·

Es seien s r die Newtonsche Summe der r-ten Potenzen der Nullstellen von y n (x;a,b) und h r eine in der Kombinatorik auftretende, homogene symmetrische Funktion der Nullstellen von y n (x;a,b) vom Grad r. Für beide werden explizite Darstellungen und Rekursionsformeln hergeleitet. Ferner werden mit Hilfe der Rekursionsformel für die y n (x;a,b) drei verschiedene Summen mit Besselpolynomen in geschlossener Form ausgewertet.

Reviewer: L.Neckermann
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33C60Hypergeometric integrals and functions defined by them
33C45Orthogonal polynomials and functions of hypergeometric type
05A19Combinatorial identities, bijective combinatorics