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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.4 Antofagasta Dec. 2016

http://dx.doi.org/10.4067/S0716-09172016000400005 

On a sequence of functions Vn (α,β,δ) (x;a, k, s)

 

Naresh K. Ajudia

Charotar University of Science Technology

Jyotindra C. Prajapati

Marwadi University

India 


ABSTRACT

In this paper, authors established various properties of a sequence offunctions {V(α,β,γ)(x;a,k,s)/n = 0,1,2,...} such as generating relations, bilateral generating relations, finite summation formulae, generating functions involving Stirling number, explicit representation and integral transforms.

Keyword : Sequence offunctions, operational techniques, generating functions, finite summationformulae, Srivastava’s theorem, Singhal-Srivastava generating function and Srivastava-Lavoie theorem.

AMS [2000] : Subject classification: 33E12, 33E99, 44A45.


REFERENCES

[1]    Buchholz, H., The Confluent Hypergeometric Function, Springer-Verlag, New York, (1969).         [ Links ]

[2]    Hubble, J. H. and Srivastava, H. M., Certain Theorem on Bilateral Generating Functions Involving Hermite, Laguerre and Gegenbauer Polynomials, Journal of Math. Anal. and Appl., 152, pp. 343-353, (1990).         [ Links ]

[3]    McBride, E. B., Obtaining Generating Functions, Springer Verlag, Berlin, (1971).         [ Links ]

[4]    Prajapati, J.C. and Ajudia, N.K., On New Sequence of Functions and Their MATLAB Computation, International J. of Phy.,Chem. and Math. Sci., 1(2), pp.24-34(2012).         [ Links ]

[5]    Riordan, J., CombinatorialIdentities, John Wiley&Sons, Inc., U.S.A., (1968).         [ Links ]

[6]    Shukla, A. K. and Prajapati, J. C., Some Properties of a Class of Polynomials Suggested by Mittal, Proyecciones Journal of Mathemat-ics, 26(2), pp. 145-156, (2007).         [ Links ]

[7]    Singhal, J. P. and Srivastava, H. M., A Class of Bilateral Generating Functions for Certain Classical Polynomials. Pacific J. Math., 42, pp. 755-762, (1972).         [ Links ]

[8]    Srivastava, H. M., Some Generalizations of Carlitz’s Theorem. Pacific J. ofMath., 85(2), pp. 471-477, (1979).

[9]    Srivastava, H. M., Some Bilateral Generating Functions for a Certain Class of Special Functions-I and II, Proc. Indag. Math., 83(2), pp. 221-246, (1980).         [ Links ]

[10]    Srivastava, H. M., Some Families of Generating Functions Associated with the Stirling Numbers of the Second Kind, Journal of Math. Anal. and Appl., 251, pp. 752-769, (2000).         [ Links ]

[11]    Srivastava, H. M. and Lavoie, J.-L., A Certain Method of Obtaining Bilateral Generating Functions, Indag. Math., 78(4), pp. 304-320, (1975).         [ Links ]

[12]    Srivastava, H. M. and Manocha, H. L., A Treatise on GeneratingFunc-tions, Ellis Harwood Limited- John Wiley and Sons, New York, (1984).         [ Links ]

Naresh K Ajudia

Department of Mathematics,

H & H B Kotak Institute of Science, Saurashtra University,

Rajkot - 360 001, Gujarat,

India

e-mail : nka121@gmail.com

Jyotindra C Prajapati

Department of Mathematics, Marwadi University,

Rajkot-Morbi Highway,

Rajkot - 360 003, Gujarat,

India

e-mail : jyotindra18@rediffmail.com

Received : March 2016. Accepted : September 2016

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