Skip to main content
Log in

New relation formula for generating functions

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. Asai, I. Kubo, H. Kuo, Multiplicative renormalization and generating functions I. Taiwan. J. Math. 7, 89–101 (2003)

    Article  MathSciNet  Google Scholar 

  2. N. Asai, I. Kubo, H. Kuo, Multiplicative renormalization and generating functions I. Taiwan. J. Math. 83, 593–628 (2004)

    Article  MathSciNet  Google Scholar 

  3. 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

    Google Scholar 

  4. P. Maroni, Semi-classical character of finite-type relations between polynomial sequences. Appl. Numer. Math. 31, 295–330 (1999)

    Article  MathSciNet  Google Scholar 

  5. P. Maroni, J. Van Iseghem, Generating functions and semiclassical orthogonal polynomials. Proc. R. Soc. Edinb. Sect. A 124(5), 1003–1011 (1994)

    Article  Google Scholar 

  6. J. Petronilho, On the linear functionals associated to linearly related sequences of orthogonal polynomials. J. Math. Anal. Appl. 315, 379–393 (2006)

    Article  MathSciNet  Google Scholar 

  7. M. Sghaier, A. Khlifi, Generating functions and a family of special orthogonal polynomials. Integral Transforms Spec. Funct. 29(1), 62–80 (2018)

    Article  MathSciNet  Google Scholar 

  8. J. Van Iseghem, Generating function, recurrence relations, differential relations. J. Comput. Appl. Math. 49, 297–303 (1993)

    MathSciNet  MATH  Google Scholar 

Download references

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wathek Chammam.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chammam, W. New relation formula for generating functions. Period Math Hung 79, 204–209 (2019). https://doi.org/10.1007/s10998-019-00290-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-019-00290-5

Keywords

Mathematics Subject Classification

Navigation