References
- Askey R. Orthogonal polynomials and special functions. Philadelphia: SIAM; 1975. (CBMS-NSF regional conference series in Appl. Math.; vol. 21).
- Andrews GE, Askey R, Roy R. Special functions. Cambridge: Cambridge University Press; 1999. (Encyclopedia of mathematics and its applications; vol. 71).
- Szwarc R. Convolution structures associated with orthogonal polynomials. J Math Anal Appl. 1992;170:158–170. doi: 10.1016/0022-247X(92)90011-2
- Ismail MEH. Classical and quantum orthogonal polynomials in one variable. Cambridge: Cambridge University Press; 2005. (Encyclopedia of mathematics and its applications; vol. 96).
- Area I, Godoy E, Rodal J, et al. Bivariate Krawtchouk polynomials: inversion and connection problems with the NAVIMA algorithm. J Comput Appl Math. 2015;284:50–57. doi: 10.1016/j.cam.2014.11.022
- Chaggara H, Mabrouk M. On inversion and connection coefficients for basic hypergeometric polynomials. Ramanujan J. 2017;46:29–48. doi: 10.1007/s11139-017-9951-0
- Ben Cheikh Y, Chaggara H. Connection coefficients via lowering operators. J Comput Appl Math. 2005;178:45–61. doi: 10.1016/j.cam.2004.02.024
- Chihara TS. An introduction to orthogonal polynomials. New York: Gordon and Breach; 1978.
- Huff WN. The type of polynomials generated by f(xt)ϕ(t). Duke Math J. 1947;14:1091–1104. doi: 10.1215/S0012-7094-47-01483-X
- Boas RP Jr, Buck RC. Polynomial expansions of analytic functions (second printing corrected). New York: Academic Press; 1964.
- Ansari KJ, Rahman S, Mursaleen M. Approximation and error estimation by modified Pältănea operators associating Gould-Hopper polynomials. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM. 2019;113:2827–2851. doi: 10.1007/s13398-019-00661-0
- Asai N, Kubo I, Kuo HH. The Brenke type generating functions and explicit forms of MRM-triples by means of q-hypergeometric series. Inf Dimens Anal Quantum Probab Related Topics. 2013;16:27 pp. doi: 10.1142/S0219025713500100
- Varma S, Sezgin S, Íçöz G. Generalization of Szász operators involving Brenke type polynomials. Comput Math Appl. 2012;64:121–127. doi: 10.1016/j.camwa.2012.01.025
- Braha NL, Mansour T, Mursaleen M. Some properties of Kantorovich-Stancu-type generalization of Szász operators including Brenke-type polynomials via power series summability method. J Funct Spaces. 2020;Article ID 3480607, 15 pp. doi: 10.1155/2020/3480607
- Mursaleen M, Ansari KJ. On Chlodowsky variant of Szász operators by Brenke type polynomials. Appl Math Comput. 2015;271:991–1003. doi: 10.1016/j.amc.2015.08.123
- Wani SA, Mursaleen M, Nisar KS. Certain approximation properties of Brenke polynomials using Jakimovski-Leviatan operators. J Inequal Appl. 2021;64:1–16. doi: 10.1186/s13660-021-02639-2
- Ben Cheikh Y. Some results on quasi-monomiality. Appl Math Comput. 2003;141:63–76. doi: 10.1016/S0096-3003(02)00321-1
- Dunkl CF. Integral kernels with reflection group invariance. Canad J Math. 1991;43:1213–1227. doi: 10.4153/CJM-1991-069-8
- Rosenblum M. Generalized Hermite polynomials and the Bose-like oscillator calculus. Oper Theory Adv Appl. 1994;73:369–396. doi: 10.1007/978-3-0348-8522-515
- Chaggara H. Operational rules and a generalized Hermite polynomials. J Math Anal Appl. 2007;332:11–21. doi: 10.1016/j.jmaa.2006.09.068
- Carlitz L. Products of Appell polynomials. Collect Math. 1963;112:133–138.
- Ben Cheikh Y, Gaied M. Dunkl-Appell d-orthogonal polynomials. Integral Transforms Spec Funct. 2007;18:581–597. doi: 10.1080/10652460701445302
- Gould HW, Hopper AT. Operational formulas connected with two generalizations of Hermite polynomials. Duke Math J. 1962;29:51–63.
- Szegö G. Orthogonal polynomials. Vol. 23. Providence (RI): Amer. Math. Soc. Colloq. Publ., Amer. Math. Soc.; 1975.
- Runge C. Über eine besondere art von intergralgleichungen. Math Ann. 1914;75:130–132. doi: 10.1007/BF01564523
- Chihara TS. Generalized Hermite polynomials [PhD thesis]. Purdue; 1955.
- Koekoek R, Lesky PA, Swarttouw RF. Hypergeometric Orthogonal polynomials and their q-analogues. Berlin: Springer; 2010. (Springer monographs in mathematics).
- Chaggara H, Koepf W. On linearization and connection coefficients for generalized Hermite polynomials. J Comput Appl Math. 2011;236:65–73. doi: 10.1016/j.cam.2011.03.010
- Chihara TS. Orthogonal polynomials with Brenke type generating functions. Duke Math J. 1968;35:505–517. doi: 10.1215/S0012-7094-68-03551-5
- Singh SN. Certain expansions for basic hypergeometric function of two variables. Math Stud. 1989;56:171–175.