Geodesic
Coefficients in Expansions of Certain Rational Functions
Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 1011-1024

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

The constant term of certain rational functions has attracted much attention recently. For example the Dyson conjecture; that the constant term of is the multinomial coefficient has spawned many generalizations (see [2], [7]). In this paper we consider some other families of rational functions which have interesting constant terms. For example, Corollary 4 states that the constant term of (1.1) is . Here, and throughout this paper, A and B denote fixed positive integers.In order to prove this result, we consider the rational function in two variables 
Evans, Ronald; Ismail, Mourad E. H.; Stanton, Dennis. Coefficients in Expansions of Certain Rational Functions. Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 1011-1024. doi: 10.4153/CJM-1982-073-1
@article{10_4153_CJM_1982_073_1,
     author = {Evans, Ronald and Ismail, Mourad E. H. and Stanton, Dennis},
     title = {Coefficients in {Expansions} of {Certain} {Rational} {Functions}},
     journal = {Canadian journal of mathematics},
     pages = {1011--1024},
     year = {1982},
     volume = {34},
     number = {4},
     doi = {10.4153/CJM-1982-073-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-073-1/}
}
TY  - JOUR
AU  - Evans, Ronald
AU  - Ismail, Mourad E. H.
AU  - Stanton, Dennis
TI  - Coefficients in Expansions of Certain Rational Functions
JO  - Canadian journal of mathematics
PY  - 1982
SP  - 1011
EP  - 1024
VL  - 34
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-073-1/
DO  - 10.4153/CJM-1982-073-1
ID  - 10_4153_CJM_1982_073_1
ER  - 
%0 Journal Article
%A Evans, Ronald
%A Ismail, Mourad E. H.
%A Stanton, Dennis
%T Coefficients in Expansions of Certain Rational Functions
%J Canadian journal of mathematics
%D 1982
%P 1011-1024
%V 34
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-073-1/
%R 10.4153/CJM-1982-073-1
%F 10_4153_CJM_1982_073_1

[1] 1. Andrews, G. E., Identities in combinatorics II: A q-analog of the Lagrange inversion theorem, Proc. Amer. Math. Soc. 53 (1975), 240–245. Google Scholar

[2] 2. Andrews, G. E., Problems and prospects for basic hyper geometric functions, in Theory and applications of special functions (Academic Press, New York, 1975), 191–240. Google Scholar

[3] 3. Andrews, G. E., Theory of partitions (Addison-Wesley, Reading, Massachusetts, 1976). Google Scholar

[4] 4. Garsia, A., A q-analogue of the Lagrange inversion formula, Houston J. Math. 7 (1981), 205–237. Google Scholar

[5] 5. Gessel, I., A noncommutative generalization and q-analoque of the Lagrange inversion formula, Transactions Amer. Math. Soc. 257 (1980), 455–482. Google Scholar

[6] 6. Jacobi, C., De resolution aequationum per series infinitas, J. fur die reine und angewandte Math. 6 (1830), 257–286. Google Scholar

[7] 7. Macdonald, I., Some conjectures for root systems, SIAM J. Math. Anal., to appear. Google Scholar

[8] 8. Mallows, C. L., A formula for expected values, Amer. Math. Monthly 87 (1980), A formula for expected values. Google Scholar

[9] 9. Rainville, E. D., Special functions (Macmillan, New York, 1960). Google Scholar

[10] 10. Sears, D., On the transformation theory of basic hyper geometric functions, Proc. London Math. Soc. 53 (1951), 158–180. Google Scholar

[11] 11. Slater, L. J., Generalized hyper geometric functions (Cambridge University Press, Cambridge, 1966). Google Scholar

[12] 12. Titchmarsh, E. C., Theory of functions, second edition (Oxford, 1944). Google Scholar

[13] 13. Zeilberger, D., A combinatorial proof of Dyson s conjecture, preprint. Google Scholar

Cité par Sources :