Abstract
In this paper, we develop a new relation between certain types of generating functions using formal algorithmic methods. As an application, we give a relation between the generating function and finite-type relations between polynomial sequences.
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N. Asai, I. Kubo, H. Kuo, Multiplicative renormalization and generating functions I. Taiwan. J. Math. 7, 89–101 (2003)
N. Asai, I. Kubo, H. Kuo, Multiplicative renormalization and generating functions I. Taiwan. J. Math. 83, 593–628 (2004)
P. Maroni, Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonaux semi-classiques, in Orthogonal Polynomials and Their Applications. Annals of Computational and Applied Mathematics, vol. 9, ed. by C. Brezinski, et al. (Baltzer, Basel, 1991), pp. 95–130
P. Maroni, Semi-classical character of finite-type relations between polynomial sequences. Appl. Numer. Math. 31, 295–330 (1999)
P. Maroni, J. Van Iseghem, Generating functions and semiclassical orthogonal polynomials. Proc. R. Soc. Edinb. Sect. A 124(5), 1003–1011 (1994)
J. Petronilho, On the linear functionals associated to linearly related sequences of orthogonal polynomials. J. Math. Anal. Appl. 315, 379–393 (2006)
M. Sghaier, A. Khlifi, Generating functions and a family of special orthogonal polynomials. Integral Transforms Spec. Funct. 29(1), 62–80 (2018)
J. Van Iseghem, Generating function, recurrence relations, differential relations. J. Comput. Appl. Math. 49, 297–303 (1993)
Acknowledgements
We are grateful to the anonymous referee for a careful reading of the text and essential remarks. The author would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project No. XXX
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Chammam, W. New relation formula for generating functions. Period Math Hung 79, 204–209 (2019). https://doi.org/10.1007/s10998-019-00290-5
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DOI: https://doi.org/10.1007/s10998-019-00290-5