Q-Analogue of a Two Variable Inverse Pair of Series with Applications to Basic Double Hypergeometric Series
Canadian journal of mathematics, Tome 41 (1989) no. 4, pp. 743-768

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

Let be a pair of a formal series (fps) in z1 and z2 of the form where is an fps with for i = 1,2. Then there exists a unique pair of fps which is also of the form (1.1), with This pair is called the inverse of f(z1,z2 ).
Krattenthaler, Christian. Q-Analogue of a Two Variable Inverse Pair of Series with Applications to Basic Double Hypergeometric Series. Canadian journal of mathematics, Tome 41 (1989) no. 4, pp. 743-768. doi: 10.4153/CJM-1989-034-1
@article{10_4153_CJM_1989_034_1,
     author = {Krattenthaler, Christian},
     title = {Q-Analogue of a {Two} {Variable} {Inverse} {Pair} of {Series} with {Applications} to {Basic} {Double} {Hypergeometric} {Series}},
     journal = {Canadian journal of mathematics},
     pages = {743--768},
     year = {1989},
     volume = {41},
     number = {4},
     doi = {10.4153/CJM-1989-034-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-034-1/}
}
TY  - JOUR
AU  - Krattenthaler, Christian
TI  - Q-Analogue of a Two Variable Inverse Pair of Series with Applications to Basic Double Hypergeometric Series
JO  - Canadian journal of mathematics
PY  - 1989
SP  - 743
EP  - 768
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-034-1/
DO  - 10.4153/CJM-1989-034-1
ID  - 10_4153_CJM_1989_034_1
ER  - 
%0 Journal Article
%A Krattenthaler, Christian
%T Q-Analogue of a Two Variable Inverse Pair of Series with Applications to Basic Double Hypergeometric Series
%J Canadian journal of mathematics
%D 1989
%P 743-768
%V 41
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-034-1/
%R 10.4153/CJM-1989-034-1
%F 10_4153_CJM_1989_034_1

[1] 1. W. A. Al-Salam, Saalschutzian theorems for basic double series, J. London. Math. Soc. 40 (1965), 455–458. Google Scholar

[2] 2. Andrews, G. E., Summations and transformations for basic Appell series, J. London Math. Soc. (2) 4 (1972), 618–622. Google Scholar

[3] 3. Andrews, G. E., Problems and prospects for basic hyper geometric functions, from Theory and Application of Special Functions (Academic Press, New York, 1975). Google Scholar

[4] 4. Burchnall, J. L. and Chaundy, T. W., Expansions of Appell s double hypergeometric functions, I and II, Quart. J. Math. Oxford Ser. II (1940), 249–270; ibid 12 (1941), 112–128. Google Scholar

[5] 5. Carlitz, L., A summation theorem for double hypergeometric series, Rend. Sem. Mat. Univ. Padova 37 (1967), 230–233. Google Scholar

[6] 6. Evans, R., Ismail, M. E. H. and Stanton, D., Coefficients in expansions of certain rational functions, Can. J. Math. 34 (1982), 1011–1024. Google Scholar

[7] 7. Gessel, I., A combinatorial proof of the multivariable Lagrange inversion formula, J. Combin. Theory A 45 (1987), 178–196. Google Scholar

[8] 8. Gessel, I.and Stanton, D., Applications of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983), 173–203. Google Scholar

[9] 9. Gessel, I.and Stanton, D., Short proofs of Saalschùtz s and Dixon's theorems, J. Combin. Theory A 38 (1985), 87–90. Google Scholar

[10] 10. Gessel, I.and Stanton, D., Another family of q-Lagrange inversion formulas, Rocky Mountain J. Math. 16 (1986), 373–384. Google Scholar

[11] 11. Hofbauer, J., A q-analogue of the Lagrange expansion, Arch. Math. 42 (1984), 536–544. Google Scholar

[12] 12. Jackson, F. H., On basic double hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 69–82. Google Scholar

[13] 13. Basic double hypergeometric functions (II), Quart. J. Math. Oxford Ser. 15 (1944), 49–61. Google Scholar

[14] 14. Jain, V. K., Some expansions involving basic hyper geometric functions of two variables, Pacific J. Math. 91 (1980), 349–361. Google Scholar

[15] 15. Krattenthaler, C., A new q-Lagrange formula and some applications, Proc. Amer. Math. Soc. 90 (1984), 338–344. Google Scholar

[16] 16. Krattenthaler, C., Operator methods and Lagrange inversion: A unified approach to Lagrange formulas, Trans. Amer. Math. Soc. 305 (1988), 431–465. Google Scholar

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

[18] 18. Srivastava, H. M., A certain class of'q-series transformations, J. Math. Anal. Appl. 107 (1985), 498–508. Google Scholar

[19] 19. Srivastava, H. M. and Jain, V. K., q-series identities and reducibility of basic double hypergeometric functions, Can. J. Math. 38 (1986), 215–231. Google Scholar

[20] 20. Srivastava, H. M., Sums of certain double q-hyper geometric series, Rend. Sem. Mat. Univ. Padova 72 (1984), 1–8. Google Scholar

Cité par Sources :