Geodesic
A Note on the Hardy-Hille and Mehler formulas
Glasgow mathematical journal, Tome 7 (1965) no. 1, pp. 55-60

Voir la notice de l'article provenant de la source Cambridge University Press

Let and Hn(x) be the nth Laguerre and Hermite polynomials, respectively. Two well-known bilinear generating formulas are the Hardy-Hille formula [1, p. 101]and the mehler formula [1, p. 377]This suggests the following problem. Consider the equationwhere fa(x) is a polynomial in x of degree n with highest coefficient equal to 1,A0 = B0 = 1. We shall also assume that ak = 1 and y0y1y2 ... yk–1 ≠ 0. We seek all sets of polynomials {fn(x)} which satisfy (1.3), (1.4) and (1.5). 
Al-Salam, W. A.; Carlitz, L. A Note on the Hardy-Hille and Mehler formulas. Glasgow mathematical journal, Tome 7 (1965) no. 1, pp. 55-60. doi: 10.1017/S204061850003519X
@article{10_1017_S204061850003519X,
     author = {Al-Salam, W. A. and Carlitz, L.},
     title = {A {Note} on the {Hardy-Hille} and {Mehler} formulas},
     journal = {Glasgow mathematical journal},
     pages = {55--60},
     year = {1965},
     volume = {7},
     number = {1},
     doi = {10.1017/S204061850003519X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S204061850003519X/}
}
TY  - JOUR
AU  - Al-Salam, W. A.
AU  - Carlitz, L.
TI  - A Note on the Hardy-Hille and Mehler formulas
JO  - Glasgow mathematical journal
PY  - 1965
SP  - 55
EP  - 60
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S204061850003519X/
DO  - 10.1017/S204061850003519X
ID  - 10_1017_S204061850003519X
ER  - 
%0 Journal Article
%A Al-Salam, W. A.
%A Carlitz, L.
%T A Note on the Hardy-Hille and Mehler formulas
%J Glasgow mathematical journal
%D 1965
%P 55-60
%V 7
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S204061850003519X/
%R 10.1017/S204061850003519X
%F 10_1017_S204061850003519X

[1] 1.Szegó, G., Orthogonal polynomials, American Mathematical Society Colloquium Publications. vol. 23, Revised edition, New York, 1959. Google Scholar

Cité par Sources :