×

Connection and duplication formulas for the Boas-Buck-Appell polynomials. (English) Zbl 1472.11085

Summary: The present paper conduct to introduce the connection and duplication formulas associated with the Boas-Buck-Appell polynomials. Examples providing the analogues results for certain members related to the Boas-Buck-Appell polynomials are considered.

MSC:

11B83 Special sequences and polynomials
68W30 Symbolic computation and algebraic computation
PDF BibTeX XML Cite
Full Text: DOI Euclid

References:

[1] M. Ali, S. Khan, Finding results for certain relatives of the Appell polynomials, Bull. Korean Math. Soc. https://doi.org/10.4134/BKMS.b180152. · Zbl 1426.33041
[2] L. C. Andrews, Special functions for engineers and applied mathematicians, Macmillan Publishing Company, New York, 1985.
[3] P. Appell, Sur une classe de polyn \({\hat{o}}\) mes, Ann. Sci. École. Norm. Sup. 9(2) (1880) 119-144.
[4] F. Avram, M. S. Taqqu, Noncentral limit theorems and Appell polynomials, Ann. Probab. 15(2) (1987) 767-775. · Zbl 0624.60049
[5] R. P. Boas, R. C. Buck, Polynomials defined by generating relations, The American Mathematical Monthly, 63(9) (1958), 626-632. · Zbl 0073.05802
[6] F. Brafman, Generating functions of Jacobi and related polynomials, Proceeding of the American Mathematica Society, 2 (1951) 942-949. · Zbl 0044.07602
[7] T. X. Chaunday, An extension of hypergeometric functions (I), Quarterly Journal of Mathematics, \bf14 (1943) 55-78.
[8] H. Chaggara, W. Koef, Duplication coefficients via generating functions, Complex Variables and Elliptic Equations, 52(6) (2007) 537-549. · Zbl 1120.33005
[9] G. Dattoli, M. Migliorati, H. M. Srivastava, Sheffer polynomials, monomiality principle, algebraic methods and the theory of classical polynomials, Math. Comput. Modelling. 45(9-10) (2007) 1033-1041. · Zbl 1117.33008
[10] Subuhi Khan, T. Nahid, Connection problems and matrix representations for certain hybrid polynomials, Tbilisi Math. J. 11(3) (2018) 81-93. · Zbl 1402.11030
[11] D. Levi, P. Tempesta, P. Winternitz, Umbral calculas, difference equations and the Schrödinger equation, J. Math. Phys. 45(11) (2004) 4077-4105. · Zbl 1064.39020
[12] S. Roman, The Umbral Calculus, Academic Press, New York, 1984. · Zbl 0536.33001
[13] H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Phil. Soc. 129 (2000) 77-84. · Zbl 0978.11004
[14] G. Szeg \(\ddot{o} \), Orthogonal polynomials, Vol. 23, 4th Edn, American Mathematical Society Colloquium (New York: American Mathematical Society), 1975.
[15] P. Tempesta, Formal groups, Bernoulli-type polynomials and L-series, C. R. Math. Acad. Sci. Paris 345(6) (2007) 303-306. · Zbl 1163.11063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.