(A) Publications in refereed
journals
(B) Conference Proceedings
(C) Review articles
(D) Books
(E) Translations
(F) Submitted articles
(G) Papers under preparetion
List of the main publications:
(A) Publications in refereed journals:
1. The
Clebsch-Gordan coefficients of the group SU(2) and Hahn polynomials,
joint with Ya. A. Smorodinskii, Soviet J. Nuclear Phys. 35 (1982)
#1, 108-113.
2. Matrix
elements of Lorentz boosts and the orthogonality of
Hahn polynomials on a contour, Soviet J. Nuclear Phys. 36 (1982)
#4, 621-622.
3. 6j-symbols
and orthogonal polynomials, joint with Ya.
A. Smorodinskii,
Soviet J. Nuclear Phys. 36 (1982) #4, 623-625.
4. Rodrigues
formula for the Racah coefficients, Soviet J. Nuclear Phys. 37
(1983) #3, 472-473.
5. The
9j-symbols as orthogonal polynomials in two discrete variables,
Soviet J. Nuclear Phys. 38 (1983) #4, 662-663.
6. The
T-coefficients of the "tree" method as orthogonal polynomials
of a discrete variable,
Soviet J. Nuclear Phys. 38 (1983) #5, 829-834.
7. The
Hahn polynomials in the Coulomb problem, Soviet J. Nuclear
Phys. 40
(1984) #1, 79-82.
8. Clebsch-Gordan
coefficients and Racah coefficients for the SU(2)
and SU(1,1) groups
as the discrete analogues of the
Poschl-Teller
potential wave functions, joint
with Yu. F. Smirnovand A. M. Shirokov,
J. Phys. A17 (1984) #11, 2157-2175.
9. Classical
orthogonal polynomials of a discrete variable and
representations of the three-dimensional rotation group,
joint with A. F. Nikiforov and
V. B. Uvarov,
Functional Anal. Appl. 19 (1985),
182-193.
10. The Hahn
and Meixner polynomials of an imaginary argument and
some of
their applications, joint
with N. M. Atakishiyev, J. Phys.
A18 (1985) #10,
1583-1596.
11. Classical
orthogonal polynomials of a discrete variableon nonuniform lattices,
joint with A. F. Nikiforov, Lett. Math. Phys. 11
(1986) \#1, 27-34.
12. Classical
orthogonal polynomials of a discrete variable
continuous orthogonality relations,
Lett. Math. Phys.14 (1987)#1,
77-88.
13. Classical
orthogonal polynomials in a discrete variable on nonuniform lattices,
joint with A. F. Nikiforov and V. B.Uvarov,
Soviet Math. Dokl. 34(1987) #3, 576-579.
14. About
one class of special functions, joint with N.
M. Atakishiyev,
Rev. Mexicana Fis. 34 (1988) #2, 152-167.
15. On the
moments of classical and related polynomials, joint with
N. M. Atakishiyev,
Rev. Mexicana Fis. 34 (1988) #2, 147-157.
16. Continuous
orthogonality property for some classical polynomials of
a discrete variable, joint
with N. M. Atakishiyev, Rev. Mexicana Fis. 34
(1988) #4, 541-563.
17. Difference
analogues of the harmonic oscillator, joint with
N. M.Atakishiyev,
Theoret. and Math. Phys. 85 (1990) #1, 1055-1062.
18. A realization
of the q-harmonic oscillator, joint with N.M.
Atakishiyev,
Theoret. and Math. Phys. 87 (1991)
#1, 442--444.
19. On the
theory of 9j-symbols, Theoret. and Math. Phys. 88(1991)
#1, 720-724.
20. On the
Askey-Wilson polynomials, joint with N.
M. Atakishiyev,
Constr. Approx. 8 (1992), 363-369.
21. The q-harmonic
oscillator and an analogue of the Charlier polynomials,
joint with R. Askey, J. Phys. A26(1993), L693-L698.
22. The q-harmonic
oscillator and the Al-Salam and Carlitz polynomials,
joint with R. Askey, Lett. Math. Phys. 29 (1993) #2, 123-132.
23. The Clebsch-Gordan
coefficients for quantum algebra SUq(2),
joint with N. M. Atakishiyev, Theoret. and Math. Phys. 98 (1994)
#1, 3-11.
24. The Pearson
equation and the beta integrals, joint with M.
Rahman,
SIAM J. Math. Anal. 25 (1994)#2, 646-693.
25. Barnes
and Ramanujan-type integrals on the q-linear lattice,
joint with M. Rahman, SIAM J. Math. Anal. 25 (1994)#3, 1002-1022.
26. On a general
q-Fourier transformation with nonsymmetric kernels,
joint with R. Askey and M. Rahman,
Journal of Computational and Applied Mathematics 68 (1996),
25-55.
27. A unified
approach to the summation and integration formulas for
q-hypergeometric functions,I,
joint with M. Rahman,
Journal of Statistical Planning and Inference
54 (1996), 101-118.
28. Some summation
theorems and transformations for q-series,
joint with M. E. H. Ismail and M. Rahman,
Canad. J. Math. 49 (1997), 543-567.
29. "Addition"
theorems for some q-exponential and q-trigonometric functions,
Methods and Applications of Analysis 4 (1997), 11-32.
30. Some orthogonal
very-well-posed 8phi7-functions,
J. Phys. A: Math. Gen.30 (1997), 5877-5885.
31. Basic
analog of Fourier series on a q-quadratic grid, joint
with J. Bustoz,
Methods and Applications of Analysis 5 (1998) #1, 1-38.
32. Multiparameter
Ramanujan-type q-beta integrals,
The Ramanujan Journal 2 (1998) # 3
.
(B)
Conference Proceedings:
1. Classical
orthogonal polynomials of a discrete variable in the theory of
group representations, joint
with A. F. Nikiforov and V. B. Uvarov,
in: Group Theoretical Methods in Physics, Vol. 1-3 (Zvenigorod,1982),
Harwood Acad. Publ., Chur, 1985, pp. 87-96.
2. Classical
orthogonal polynomials of a discrete variable on nonuniform lattices,
joint with A. F. Nikiforov, in:
GroupTheoretical Methods in Physics, Vol.1
(Yurmala, 1985), VNU Sci. Press,
Utrecht, 1986, pp. 505-511.
3. Representations
of SO(3,1) and the Hahn polynomials, joint
with N. M. Atakishiyev,
in: Group Theoretical Methods in Physics, Vol. 1 (Yurmala, 1985),
VNU Sci. Press, Utrecht, 1986, pp.
523-530.
4. The
Charm polynomials, joint with N. M. Atakishiyev and G.
I. Kuznetsov,
in: Proceedings of the Third International Symposium on Orthogonal Polynomials
and Their Applications (Brezinski et al., eds.), J. C. Baltzer A. G., Basel,
Switzerland, 1991, pp. 15-16.
5. Classical
biorthogonal rational functions, joint with M.
Rahman,
in: Methods of Approximation Theory in
Complex Analysis and Mathematical Physics
(A. A. Gonchar and E. B. Saff, eds.), Lecture
Notes in Math. Vol. 1550,
Springer-Verlag, 1993, pp. 131-146.
6. An
analog of the Fourier transformation for a q-harmonic oscillator,
joint with R.Askey and N. M. Atakishiyev, in:
Symmetries in Science VI (B. Gruber, ed.),
Plenum Press, New York, 1993, pp. 57-63;
Preprint IAE-5611/1, Kurchatov Institute, Moscow 1993.
7. Singular
analogue of the Fourier transformation for the
Askey-Wilson polynomials,
joint with M. Rahman, in: Symmetries
and Integrability of Difference Equations
(D. Levi, L. Vinet, and P. Winternitz, eds.),
CRM Proceedings & Lecture Notes,
Vol.9,
American Math. Society, 1996, pp. 289-302.
8. Some
generating functions for q-polynomials, joint
with M. Ismail and D. Masson,
in: Special Functions, q-Series and Related Topics
(M. E. H. Ismail, D. R. Masson, and M. Rahman, eds.),
Fields Institute Communications, Vol. 14, American Math. Society,
1997, pp. 91-108.
1. On
the theory of difference analogues of special functions of
hypergeometric type,
Russian Math. Surveys 44 (1989) #2, 227-278, London Math. Soc.
2. Difference
hypergeometric functions, joint with N.
M. Atakishiyev,
in: Progress in Approximation Theory: An
International Perspective
(A. A. Gonchar and E. B. Saff, eds.), Springer
Series in Computational Mathematics,
Vol. 19, Springer-Verlag, 1992, pp. 1-35.
3. On
the classical orthogonal polynomials, joint with N.
M. Atakishiyev and M. Rahman,
Constr. Approx.11 (1995)
#2, 181-226.
1. Classical
Orthogonal Polynomials of a Discrete Variable,
joint with A. F. Nikiforov and V. B. Uvarov, Nauka,
Moscow, 1985;
English translation in Springer Series in Computational Physics,
Springer-Verlag, 1991.
(E)
Translations:
1. Askey,
R. Ramanujan and hypergeometric and basic hypergeometric
series[in Russian],
translated from English with remark by N. M. Atakishiyev and S. K. Suslov,
Uspekhi Mat. Nauk 45 (1990)
#1, 33-76; Russian Math. Surveys 45 (1990) #1,
37-86,
London Math. Soc.
2. Gasper,
G. and Rahman, M. Basic Hypergeometric Series [in Russian], translated
from English
by N. M.Atakishiyev and S. K. Suslov, Mir, Moscow, 1993.
1. A
unified approach to the summation and integration formulas
for q-hypergeometric functions. II-III, joint
with M. Rahman,
submitted to Methods and Applications of
Analysis.
2. The
q-Bessel functions on a q-quadratic grid,
joint with M. E. H. Ismail and D. Masson,
to appear in the Proceedings of CRM workshop
on algebraic methods and q-special functions, Montreal, May
1996.
(G)
Papers under preparetion:
1.
Askey-Wilson type operators and their inverses,
joint with M. E. H. Ismail and M. Rahman.
2.
Properties of a q-analogue of Bessel functions,
joint with M. E. H. Ismail and D. Masson.
3.
An Introduction to Special Functions, 33 latex pages.
4.
Some orthogonal very-well-poised 8phi7-functions
that generalize Askey--Wilson polynomials,
MSRI Preprint No. 1997-060, Berkeley,California, 1997, 31 pp;
see also http://lefty.msri.org/publications/preprints/online/1997-070.html.
5.
Basic Fourier series expansions of certain functions, joint
with J. Bustoz.
6.
Note on a q-Bessel function.