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Volumn 123, Issue 1, 2003, Pages 125-146

q-Taylor theorems, polynomial expansions, and interpolation of entire functions

Author keywords

Askey Wilson operators; Carlson's theorem; Integral representations; Polynomial bases; q exponential function; q Taylor series

Indexed keywords


EID: 5044240397     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9045(03)00076-5     Document Type: Article
Times cited : (56)

References (23)
  • 2
    • 0013269433 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • Memoirs of the American Mathematical Society, 319. Providence RI
    • R.A. Askey, J.A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Memoirs of the American Mathematical Society, 319. Providence RI, 1985.
    • (1985)
    • Askey, R.A.1    Wilson, J.A.2
  • 3
    • 0004032164 scopus 로고
    • Entire Functions
    • Academic Press, New York
    • R.P. Boas, Entire Functions, Academic Press, New York, 1954.
    • (1954)
    • Boas, R.P.1
  • 5
    • 30244433646 scopus 로고    scopus 로고
    • 5 summation formula
    • preprint, March
    • 5 summation formula, preprint, March 1996.
    • (1996)
    • Cooper, S.1
  • 6
    • 0037736197 scopus 로고    scopus 로고
    • Elementary derivations of summation and transformation formulas for q-series
    • M.E.H. Ismail, D.R. Masson, M. Rahman (Eds.), American Mathematical Society, Providence, RI
    • G. Gasper, Elementary derivations of summation and transformation formulas for q-series, in: M.E.H. Ismail, D.R. Masson, M. Rahman (Eds.), Special Functions, q-Series and Related Topics, Fields Institute Communication, Vol. 14, American Mathematical Society, Providence, RI, 1997, pp. 55-70.
    • (1997) Special Functions, Q-Series and Related Topics, Fields Institute Communication , vol.14 , pp. 55-70
    • Gasper, G.1
  • 8
    • 0004258303 scopus 로고
    • Translated from the Russian, Hindustan Publishing Corporation, Delhi
    • A.O. Gelfond, Calculus of Finite Differences, Translated from the Russian, Hindustan Publishing Corporation, Delhi, 1971.
    • (1971) Calculus of Finite Differences
    • Gelfond, A.O.1
  • 9
    • 0004009742 scopus 로고
    • Ramanujan: Twelve Lectures on Subjects Suggested by his Life and Work
    • Chelsea, New York
    • G.H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by his Life and Work, Chelsea, New York, 1978.
    • (1978)
    • Hardy, G.H.1
  • 10
    • 84968495088 scopus 로고
    • Difference equations: Disconjugacy, principal solutions, Green's functions, complete monotonicity
    • P. Hartman, Difference equations: disconjugacy, principal solutions, Green's functions, complete monotonicity, Trans. Amer. Math. Soc. 246 (1978) 1-30.
    • (1978) Trans. Amer. Math. Soc. , vol.246 , pp. 1-30
    • Hartman, P.1
  • 11
    • 0012746951 scopus 로고
    • The Askey-Wilson operator and summation theorems
    • M. Ismail, M.Z. Nashed, A. Zayed, A. Ghaleb (Eds.), American Mathematical Society, Providence, RI
    • M.E.H. Ismail, The Askey-Wilson operator and summation theorems, in: M. Ismail, M.Z. Nashed, A. Zayed, A. Ghaleb (Eds.), Mathematical Analysis, Wavelets, and Signal Processing, Contemporary Mathematics, Vol. 190, American Mathematical Society, Providence, RI, 1995, pp. 171-178.
    • (1995) Mathematical Analysis, Wavelets, and Signal Processing, Contemporary Mathematics , vol.190 , pp. 171-178
    • Ismail, M.E.H.1
  • 14
    • 0001865725 scopus 로고
    • Diagonalization of certain integral operators
    • M.E.H. Ismail, R. Zhang, Diagonalization of certain integral operators, Adv. Math. 109 (1994) 1-33.
    • (1994) Adv. Math. , vol.109 , pp. 1-33
    • Ismail, M.E.H.1    Zhang, R.2
  • 15
    • 85031157018 scopus 로고    scopus 로고
    • New proofs of some q-series results
    • M.E.H. Ismail, H. Koelink (Eds.), Kluwer, to appear
    • M.E.H. Ismail, R. Zhang, New proofs of some q-series results, in: M.E.H. Ismail, H. Koelink (Eds.), Kluwer, to appear.
    • Ismail, M.E.H.1    Zhang, R.2
  • 16
    • 30244487216 scopus 로고
    • The theory of coordinates
    • a book manuscript
    • B.H. Makar, The theory of coordinates, a book manuscript, 1973.
    • (1973)
    • Makar, B.H.1
  • 17
    • 0002110514 scopus 로고
    • Über ganzwertige ganze Funktionen
    • G. Polya, Über ganzwertige ganze Funktionen, Ren. Circ. Mat. Palermo 40 (1915) 1-16.
    • (1915) Ren. Circ. Mat. Palermo , vol.40 , pp. 1-16
    • Polya, G.1
  • 19
    • 0002114140 scopus 로고
    • About the growth of entire functions solutions of linear algebraic q-difference equations
    • J.P. Ramis, About the growth of entire functions solutions of linear algebraic q-difference equations, Ann. Fac. Sc. Toulouse 1 (6) (1992) 53-94.
    • (1992) Ann. Fac. Sc. Toulouse , vol.1 , Issue.6 , pp. 53-94
    • Ramis, J.P.1
  • 20
    • 5044236184 scopus 로고
    • On entire functions assuming integer values in a geometric sequence
    • (Quebec, PQ, 1987), de Gruyter, Berlin
    • R.V. Wallisser, On entire functions assuming integer values in a geometric sequence, in: Théorie des Nombres (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 981-989.
    • (1989) Théorie des Nombres , pp. 981-989
    • Wallisser, R.V.1
  • 21
    • 0004262752 scopus 로고
    • 4th Edition, Cambridge University Press, Cambridge
    • E.T. Whittaker, G.N. Watson, Modern Analysis, 4th Edition, Cambridge University Press, Cambridge, 1927.
    • (1927) Modern Analysis
    • Whittaker, E.T.1    Watson, G.N.2
  • 22
    • 0003947483 scopus 로고
    • Cambridge Tracts in Mathematics and Mathematical Physics, No. 33, Cambridge
    • J.M. Whittaker, Interpolatory Function Theory, Cambridge Tracts in Mathematics and Mathematical Physics, No. 33, Cambridge, 1935.
    • (1935) Interpolatory Function Theory
    • Whittaker, J.M.1
  • 23
    • 0038197593 scopus 로고
    • Sur les Séries de Base de Polynomes Quelconques
    • Gauthier-Villars, Paris
    • J.M. Whittaker, Sur les Séries de Base de Polynomes Quelconques, Gauthier-Villars, Paris, 1949.
    • (1949)
    • Whittaker, J.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.