Advanced search
Publication Cover
Integral Transforms and Special Functions Volume 33, 2022 - Issue 6
Submit an article Journal homepage
119
Views
1
CrossRef citations to date
0
Altmetric
Research Articles

Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

Min-Jie Luoa Department of Mathematics, College of Science, Donghua University, Shanghai, People's Republic of China;b Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, People's Republic of ChinaCorrespondence[email protected] [email protected]
ORCID Iconhttps://orcid.org/0000-0001-7433-4490View further author information
ORCID Icon,
Ravinder Krishna Rainac M.P. University of Agriculture and Technology, Udaipur, Rajasthan, IndiaView further author information
&
Shu-Han Zhaoa Department of Mathematics, College of Science, Donghua University, Shanghai, People's Republic of ChinaView further author information
Pages 496-512 | Received 02 Apr 2021, Accepted 17 Jul 2021, Published online: 26 Jul 2021

References

  • Luo M-J, Raina RK. Generating functions of Pollaczek polynomials: a revisit. Integral Transform Spec Funct. 2019;30:893–919.
  • Srivastava HM, Karlsson PW. Multiple Gaussian hypergeometric series. Chichester: Ellis Horwood Ltd.; 1985.
  • Ismail MEH. Classical and quantum orthogonal polynomials in one variable Vol. 98. New York: Cambridge University Press; 2009.
  • Brychkov YuA. Reduction formulas for the Appell and Humbert functions. Integral Transform Spec Funct. 2017;28:22–38.
  • Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and series. More special functions. Vol. 3. New York (NY): Gordon and Breach; 1990.
  • Srivastava HM, Manocha HL. A treatise on generating functions. New York: Halsted Press (Chichester: Ellis Horwood Limited), John Wiley and Sons; 1984; Chichester, Brisbane, and Toronto.
  • Ahbli K, Mouayn Z. A generating function and formulae defining the first associated Meixner Pollaczek polynomials. Integral Transform Spec Funct. 2018;29:352–366.
  • Ismail MEH, Letessier J, Valent G. Linear birth and death models and associated Laguerre and Meixner polynomials. J Approx Theory. 1988;55:337–348.
  • Luo M-J, Wong R. Asymptotics of the associated Pollaczek polynomials. Proc Amer Math Soc. 2019;147(6):2583–2597.
  • Pollaczek F. Sur une famille de polynômes orthogonaux à quatre paramètres. C R Acad Sci Paris. 1950;230:2254–2256.
  • Ferreira C, López JL, Sinusía EP. The third Appell function for one large variable. J Approx Theory. 2013;165:60–69.
  • Olver FWJ, Lozier DW, Boisvert RF, et al., editors. NIST handbook of mathematical functions. New York: Cambridge University Press; 2010.
  • Erdélyi A, Magnus W, Oberhettinger F, et al. Higher transcendental functions. Vol. I. New York: McGraw-Hill; 1981.
  • Erdélyi A, Magnus W, Oberhettinger F, et al. Higher transcendental functions. Vol. II. New York: McGraw-Hill; 1981.
  • Atakishiyev NM, Suslov SK. The Hahn and Meixner polynomials of an imaginary argument and some of their applications. J Phys A. 1985;18:1583–1596.
  • Letessier J, Ronveaux A, Valent G. Fourth-order difference equation for the associated Meixner and Charlier polynomials. J Comput Appl Math. 1996;71:331–341.
  • Erdélyi A, Magnus W, Oberhettinger F, et al. Higher transcendental functions. Vol. III. New York: McGraw-Hill; 1981.
  • Chan W-Ch-C, Chyan Ch-J, Srivastava HM. The Lagrange polynomials in several variables. Integral Transform Spec Funct. 2001;12:139–148.
  • Chen K-Y, Liu S-J, Srivastava HM. Some new results for the Lagrange polynomials in several variables. ANZIAM J. 2007;49:243–258.
  • Ismail MEH. Encyclopedia of special functions: the Askey-Bateman project: volume 1 – univariate orthogonal polynomials. Cambridge (MA): Cambridge University Press; 2020.
  • Rahman M. A generalization of Gasper's kernel for Hahn polynomials: application to Pollaczek polynomials. Canad J Math. 1978;30(1):133–146.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.