Summary
A study of various properties of those sets of polynomials which satisfy(1.2) below is made.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Beferences
W. A. Al-Salam andL. Carlitz,Some orthogonal q-polynomials, Mathematische Nachrichten, vol. 30 (1965), pp. 47–61.
P. Appell,Une Classe de polynomes, Annales scientifique Ecole Normale Sup., ser. 2, vol. 9 (1880), pp. 119–144.
L. Carlitz,Note on orthogonal polynomials related to theta functions, Publicationes Mathematicae, vol. 5 (1958), pp. 222–228.
—— ——,Some polynomials related to theta functions, Annali di Matematica pura ed applicata, ser. 4, vol. 41 (1955), pp. 359–373.
H. T. Davis,The Theory of Linear Operators, The Principia Press, (1936).
L. Euler,Introductio in Analysin Infinitorum, (1748), (Chapter 7).
L. Ya. Geronimus,Polynomials Orthogonal on a Circle and Interval, Pergamon Press, (1960).
W. Hahn,Über Orthogonal polynome, dieq-Differenzengleichungen genigen, Mathematische Natchrichten, vol. 2 (1949), pp. 4–34.
A. Sharma andA. Chak,The basic analogue of a class of polynomials, Rivista di Matematica della Università di Parma, vol. 5 (1954), pp. 325–337.
I.M. Sheffer,On sets of polynomials and associated linear functional operator and equations, The American Journal of Mathematics, vol. 53 (1931), pp. 15–38.
—— ——,Note on Appell polynomials, Bulletin of the American Mathematical Society, vol. 51 (1945), pp. 739–744.
G. Szedö,Ein Beitrag zur Theorie der Thetafunktionen, Preussische Akademie der Wissenschaften, Sitzung der phys.-math. Klasse, (1926), pp. 242–251.
-- --,Orthogonal Polynomials, American Mathematical Society Colloquim Publications, revised edition, New York, (1959).
L. Toscano,Polinomi orthogonali o reciproci di ortogonali nella classe di Appell, Le Matematiche, vol. 11 (1956), pp. 168–174.
R.S. Varma,On Appell polynomials, Proceedings of the American Mathematical Society, vol. 2 (1951), pp. 593–596.
M. Ward,A calculus of sequences, American Journal of Mathematics, vol. 58, (1936), pp. 255–266.
S. Wigert,Sur les polynomes orthogonaux et l'approximation des fractions continues, Archiv for Mathematik och Eysik, vol. 17 (1923), no. 18.
Rights and permissions
About this article
Cite this article
Al-Salam, W.A. q-Appell polynomials. Annali di Matematica 77, 31–45 (1967). https://doi.org/10.1007/BF02416939
Issue Date:
DOI: https://doi.org/10.1007/BF02416939