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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.36 no.3 Antofagasta Sept. 2017

http://dx.doi.org/10.4067/S0716-09172017000300545 

Articles

Corrigendum

A. K. Shukla1 

S. J. Rapeli2 

1 S. V. National Institute of Technology, Department of Mathematics, Surat-395 007, India, e-mail: ajayshukla2@rediffmail.com

2 S. V. National Institute of Technology, Department of Mathematics, Surat-395 007, India, e-mail: shrinu0711@gmail.com

Corrigendum to “An Extension of Sheffer Polynomials”

(Proyecciones Journal of Mathematics, Vol. 30, No 2, pp. 265 - 275)

We regret to announce that there are some mathematical errors in theorem 2.3 and theorem 2.4. Our aim to correct and modify the theorem 2.3 and theorem 2.4.

Brown (1) stated that {B n(x)} is a polynomial sequence which is simple and of degree precisely n. {B n(x)} is a binomial sequence if

and a simple polynomial sequence { Pn (x)} is a Sheffer sequence if there is a binomial sequence {B n(x)} such that

Theorem 2.3: Let pn (x,y) be symmetric, a class of polynomials in two variables and Sheffer A-type zero which belong to the operator J(D) and have the generating function as equation (1.11) of theorem 2.1 (See (2)). There exist sequences and η k, independent of x, y and n, such that for all n ≥ 1,

where μk = (k + 1)g k in terms of g k of equation (1.8) and η k = (k + 1) h k, in terms of h k of equation (1.9).

Proof: Let (See ((2)))

Thus we get

This gives the proof of statement.

Theorem 2.4: A necessary and sufficient condition that pn (x,y) be of Sheffer A-type zero, there exists sequence gk and hk , independent of x,y and n, such that

Where pn (x,y) is symmetric and a class of polynomials in two variables.

Proof: Let (See ((2))

Thus

References:

[1] J. W. Brown, On multivariable Sheffer sequences, J. Math. Anal. Appl., Vol. 69, (1979), pp.398-410. [ Links ]

[2] A. K. Shukla and S. J. Rapeli, An Extension of Sheffer Polynomials, Proyecciones Journal of Mathematics, Vol. 30, No. 2 (2011), pp. 265-275. [ Links ]

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