An extension of sheffer polynomials

Authors

  • Ajay K. Shukla S. V. National Institute of Technology.
  • S. J. Rapeli S. V. National Institute of Technology.

DOI:

https://doi.org/10.4067/S0716-09172011000200009

Keywords:

Appell sets, Differential operator, Sheffer polynomials, Generalized Sheffer polynomials.

Abstract

Sheffer [Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), pp.590-622] studied polynomial sets zero type and many authors investigated various properties and its applications. In the sequel to the study of Sheffer Polynomials, an attempt is made to generalize the Sheffer polynomials by using partial differential operator.

References

[1] W. A. Al Salam and A. Verma, Generalized Sheffer Polynomials, Duke Math. J. 37, pp. 361-365, (1970).

[2] B. Alidad, On some problems of special functions and structural matrix analysis, Ph.D. diss., Aligarh Muslim University, (2008).

[3] Joseph D. Galiffa, The Sheffer B-type 1 orthogonal polynomial sequences, Ph.D. diss., University of Central Florida, (2009).

[4] William N. Huff and E. D. Rainville, On the Sheffer A-type of polynomials generated by Φ(t)f(xt), Proc. Amer. Math. Soc. 3, pp. 296-299 (1952).

[5] E. B. Mc Bride, Obtaining Generating Functions, Springer, New York, (1971).

[6] V. B. Osegove, Some extremal properties of generalized Appell polynomials, Soviet Math. Five, pp. 1651-1653, (1964).

[7] E. D. Rainville, Special Functions, the Macmillan Company, New York, (1960).

[8] I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5, pp. 590-622, (1939).

[9] J. F. Steffensen, The Poweroid, an extension of the mathematical notion of power, Acta Math. 73, pp. 333-366, (1941).

Published

2011-12-09

How to Cite

[1]
A. K. Shukla and S. J. Rapeli, “An extension of sheffer polynomials”, Proyecciones (Antofagasta, On line), vol. 30, no. 2, pp. 265-275, Dec. 2011.

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