Generalized Sheffer's Classification and Their q-Analague

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Authors

  • R. K. Jana
     Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395 007 ,IN
  • S. J. Rapeli
     Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395 007 ,IN
  • A. K. Shukla
     Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395 007 ,IN

DOI:

https://doi.org/10.18311/jims/2017/14851

Keywords:

Differential Operator, Sheer Polynomials, q-analogue of Sheer Polynomials

Abstract

Polynomial sets of type zero and its properties together with various applications were studied in the past. In the Rota theory, the polynomials of Sheer A-type zero are called Sheer sequences. In particular, members of the q-analogue of the Sheer class A-type zero can be called q-Sheer sequences. In the present paper, an attempt is made to discuss q-analogues of generalized Sheer polynomials in two variables and their properties.

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Published

2017-07-01

How to Cite

Jana, R. K., Rapeli, S. J., & Shukla, A. K. (2017). Generalized Sheffer’s Classification and Their q-Analague. The Journal of the Indian Mathematical Society, 84(3-4), 201–210. https://doi.org/10.18311/jims/2017/14851

Issue

Volume 84, Issue 3-4, July-December 2017

Section

Articles

License

Copyright (c) 2017 R. K. Jana, S. J. Rapeli, A. K. Shukla

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Received 2017-02-03
Accepted 2017-02-15
Published 2017-07-01

 

References

W. A. Al-Salam, q-Appell polynomials, Ann. Mat. Pura Appl., 77 (4) (1967), 31-45.

W. A. Al Salam and A. Verma, Generalized Sheer polynomials, Duke Math. J., 37 (1970), 361-365.

W. A. Al-Salam and M. E. H. Ismail, q-beta integrals and the q-Hermite polynomials, Pacic J. Math., 135 (2) (1988), 209-221.

B. Alidad, On some problems of special functions and structural matrix analysis, Ph.D. Dissertation, Aligarh Muslim University, 2008.

G. E. Andrews, On the foundations of combinatorial theory V, Eulerian differential operators, Studies in Appl. Math., 50 (1971), 345-375.

G. Bretti, C. Cesarano and P. E. Ricci, Laguerre-type exponentials and generalized Appell polynomials, Computers Math. Applic., 48 (2004), 833-839.

J. W. Brown, On the Sheer A-type of certain modified polynomial sets, Proc. Amer. Math. Soc., 23 (1969), 718-722.

J. W. Brown, On multivariable Sheer sequences, J. Math. Anal. Appl., 69 (1979), 398-410.

A. M. Chak, An extension of a class of polynomials I, Riv. Mat. Univ. Parma, 2 (12) (1971), 47-55.

A. M. Chak and A. K. Agarwal, An extension of a class of polynomials II, SIAM J.Math. Anal., 2 (1971), 352-355.

A. M. Chak and H. M. Srivastava, An extension of a class of polynomials III, Riv. Mat.Univ. Parma, 3 (2) (1973), 11-18.

Gi-Sang Cheon and Ji-Hwan Jung, The q-Sheer sequences of a new type and associated orthogonal polynomials, Linear Algebra Appl., 491 (2016), 171-186.

J. D. Galia, The Sheer B-type 1 orthogonal polynomial sequences, Ph.D. Dissertation, University of Central Florida, USA, 2009.

G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, 1990.

J. L. Goldberg, On the Sheer A-type of polynomials generated by A(t)ψ(xB (t)), Proc. Amer. Math. Soc., 17 (1966), 170-173.

W. N. Huff and E. D. Rainville, On the Sheer A-type of polynomials generated by Φ(t)f(xt), Proc. Amer. Math. Soc., 3 (1952), 296-299.

M. E. H. Ismail, Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005.

M. E. H. Ismail, An operator calculus for the Askey-Wilson operator, Ann. Comb., 5 (2001), 347-362.

M. E. H. Ismail, Theory and Applications of Special Functions: A Volume Dedicated to Mizan Rahman, Springer, New York, USA, 2005.

S. Khan and M. Riyasat, A determinantal approach to Sheffer-Appell polynomials via monomiality principle, J. Math. Anal. Appl., 421 (1) (2015), 806-829.

S. Khan, G. Yasmin and M. Riyasat, Certain results for the 2-variable Apostol type and related polynomials, Comput. Math. Appl., 69 (11) (2015), 1367-1382.

V. B. Osegove, Some extremal properties of generalized Appell polynomials, Soviet Math., 5 (1964), 1651-1653.

E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

S. J. Rapeli and A. K. Shukla, A note on α-type polynomial sets, Integral Transforms Spec. Funct., 25 (3) (2014), 249-253.

A. Sharma and A. M. Chak, The basic analogue of a class of polynomials, Riv. Mat.Univ. Parma, 5 (1954), 325-337.

I. M. Sheer, Some properties of polynomial sets of type zero, Duke Math. J., 5 (1939), 590-622.

I. M. Sheer, Some applications of certain polynomial classes, Bull. Amer. Math. Soc., 47 (1941), 885-898.

I. M. Sheer, Note on Appell Polynomials, Bull. Amer. Math. Soc., 51 (1945), 739-744.

H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press, New York, 1984.

H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, Amsterdam, 2012.

J. F. Steensen, The Poweroid, an extension of the mathematical notion of power, Acta Math., 73 (1941), 333-366.