Bibliography

BIBLIOGRAPHY

Research interests: Classical analysis and approximation theory, orthogonal polynomials and q-special functions, theory of group representations, integral transformations and their applications, computer algebra and special functions.

Contents

(A) Publications in refereed journals
(B) Conference proceedings
(C) Review articles
(D) Books
(E) Translations
(F) Submitted articles
(G) Papers under preparetion
(H) Web pages design

List of 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. 84c:81022
     2. Matrix elements of Lorentz boosts and the orthogonality of Hahn polynomials on a contour, Soviet J. Nuclear Phys. 36 (1982) # 4, 621-622. 84m:33024
     3. 6j-symbols and orthogonal polynomials, joint with Ya. A. Smorodinskii, Soviet J. Nuclear Phys. 36 (1982) # 4, 23-625. 84f:81036
     4. Rodrigues formula for the Racah coefficients, Soviet J. Nuclear Phys. 37 (1983) # 3, 472-473. 85d:81054
     5. The 9j-symbols as orthogonal polynomials in two discrete variables, Soviet J. Nuclear Phys. 38 (1983) # 4, 662-663. 85g:81074
     6. The T-coefficients of the "tree" method as orthogonal polynomials of a discrete variable, Soviet J. Nuclear Phys. 38 (1983) # 5, 829-834. 86d:33017
     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 Pöschl-Teller potential wave functions, joint with Yu. F. Smirnovand A. M. Shirokov, J. Phys. A17 (1984) # 11, 2157-2175. 86g:81059
     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. 87d:33026
    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. 87i:33021
    11. Classical orthogonal polynomials of a discrete variableon nonuniform lattices, joint with A. F. Nikiforov, Lett. Math. Phys. 11(1986) #1, 27-34. 87c:33014
    12. Classical orthogonal polynomials of a discrete variable continuous orthogonality relations, Lett. Math. Phys. 14 (1987) # 1, 77-88. 88h:33029
    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. 88b:39003
    14. About one class of special functions, joint with N. M. Atakishiyev, Rev. Mexicana Fis. 34 (1988) #2, 152-167. 91e:33001
    15. On the moments of classical and related polynomials, joint with N. M. Atakishiyev, Rev. Mexicana Fis. 34 (1988) # 2, 147-157. 92a:33004
    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. 1 034 478
    17. Difference analogues of the harmonic oscillator, joint with N. M.Atakishiyev, Theoret. and Math. Phys. 85 (1990) # 1, 1055-1062. 92i:81035
    18. A realization of the q-harmonic oscillator, joint with N.M. Atakishiyev, Theoret. and Math. Phys. 87 (1991) # 1, 442-444. 92e:81086
    19. On the theory of 9j-symbols, Theoret. and Math. Phys. 88(1991) # 1, 720-724. 92i:81089
    20. On the Askey-Wilson polynomials, joint with N. M. Atakishiyev, Constr. Approx. 8 (1992), 363-369. 93h:33011
    21. The q-harmonic oscillator and an analogue of the Charlier polynomials, joint with R. Askey, J. Phys. A26(1993), L693-L698. 94j:33031
    22. The q-harmonic oscillator and the Al-Salam and Carlitz polynomials, joint with R. Askey, Lett. Math. Phys. 29 (1993) # 2, 123-132. 94j:33032
    23. The Clebsch-Gordan coefficients for quantum algebra SUq(2), joint with N. M. Atakishiyev, Theoret. and Math. Phys. 98 (1994) # 1, 3-11. 95g:17014
    24. The Pearson equation and the beta integrals, joint with M. Rahman, SIAM J. Math. Anal. 25 (1994)# 2, 646-693. 95f:33001
    25. Barnes and Ramanujan-type integrals on the q-linear lattice, joint with M. Rahman, SIAM J. Math. Anal. 25 (1994) # 3, 1002-1022. 95e:33022
    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. 98m:42033
    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. 98c:33018
    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. 98e:33005
    29. "Addition" theorems for some q-exponential and q-trigonometric functions, Methods and Applications of Analysis 4 (1997), 11-32. 98i:33023
    30. Some orthogonal very-well-posed 8phi7-functions, J. Phys. A: Math. Gen.30 (1997), 5877-5885. 98m:33047
    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. 99e:33020
    32. Multiparameter Ramanujan-type q-beta integrals, The Ramanujan Journal 2 (1998) # 3, 351-369. 99j:33020
    33. A unified approach to the summation and integration formulas for q-hypergeometric functions. II, joint with M. Rahman, Methods and Applications of Analysis 5 (1998) # 4, 399-412. 2000a:33024
    34. A unified approach to the summation and integration formulas for q-hypergeometric functions. III, joint with M. Rahman, Methods and Applications of Analysis 5 (1998) # 4, 413-424. 2000a:33024
    35. Another addition theorem for the q-exponential function, J. Phys. A: Math. Gen. 33 (2000) L375-L380.

(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. 989 284
     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. 946 899
     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. 946 901
     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. 95f:33007
     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. 95m:42034
     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; 1 258 093; 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. 98b:33037
     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. 98d:33012
     9. The q-Bessel functions on a q-quadratic grid, joint with M. E. H. Ismail and D. Masson, in: Algebraic Methods and q-Special Functions (J. F. van Diejen and L. Vinet, eds.), CRM Proceedings & Lecture Notes, Vol. 22, American Math. Society, 1999, pp. 183-200.
    10. Numerical investigation of basic Fourier series, joint with R. Wm. Gosper, in: q-Series from a Contemporary Rerspective (M. E. H. Ismail and D. W. Stanton, eds.), Contemporary Mathematics, Vol. 254, American Math. Soc; 2000, pp. 199-227.

(C) Review articles:

     1. On the theory of difference analogues of special functions ofhypergeometric type, Uspekhi Mat. Nauk 44 (1989) # 2(266), 185--226; translation in Russian Math. Surveys 44 (1989) #2, 227-278, London Math. Soc. 91a:33015. See also: Letter to the editors: "On the theory of difference analogues of special functions of hypergeometric type" ; Uspekhi Mat. Nauk 45 (1990) # 3(273), 219; translation in Russian Math. Surveys 45 (1990) # 3, 2451 071 948
     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. 94k:33039
     3. On the classical orthogonal polynomials, joint with N. M. Atakishiyev and M. Rahman, Constractive Approximation 11(1995) #2, 181-226. 96i:33029

(D) Books:

1. Classical Orthogonal Polynomials of a Discrete Variable, joint with A. F. Nikiforov and V. B. Uvarov, Nauka, Moscow, 1985 87f:33001; English translation in Springer Series in Computational Physics, Springer-Verlag, 1991. 92m:33019
2. {\cyr Klassicheskie ortogonal\cprime nye polinomy}. (Russian) [Classical orthogonal polynomials], joint with A. F. Nikiforov, {\cyr Novoe v Zhizni, Nauke, Tekhnike: Seriya "Matematika, Kibernetika"} [Current Life, Science andTechnology: Series "Mathematics and Cybernetics"], 85-12. ``Znanie'', Moscow, 1985. 32 pp. 87e:33015

(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. 92k:01020
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. 95d:33017

(F) Submitted articles:

     1. Some expansions in basic Fourier series and related topics, 47 latex pp., submitted to The Journal of Approximation Theory.
     2. Some orthogonal very-well-poised 8phi7-functions that generalize Askey-Wilson polynomials, 31 latex pp., to appear in the Ramanujan Journal; see alsohttp://lefty.msri.org/publications/preprints/online/1997-070.html.
     3. Asymptotics of zeros of basic sine and cosine functions, 15 latex pp., submitted to Constructive Approximation.
     4. Basic exponential functions on a q-quadratic grid, 41 latex pp., to appear.
     5. Basic Fourier series and q-Euler polynomials, 21 latex pp., submitted to The Ramanujan Journal.
     6. Completeness of basic trigonometric system in L^p, 16 latex pp., submitted.
     7. A note on completeness of basic trigonometric system in L^2, 10 latex pp., submitted to Rocky Mountain Journal of Mathematics.

(G) Papers under preparetion:

     1. Askey-Wilson type operators and their inverses I-III, joint with M. E. H. Ismail and M. Rahman.
     2. An Introduction to Special Functions, 33 latex pages.
     3. Note on a q-Bessel function.

(H) Web pages design:

1. The Linear Algebra Home Page, Department of Mathematics, Arizona State University. http://www.public.asu.edu/~sergei/linalg/LinAlg.html
2. The NATO Advanced Study Instituite: Special Functions 2000
http://math.la.asu.edu/~sf2000/index.html