On a sequence of functions Vn (α,β,δ) (x;a, k, s)
DOI:
https://doi.org/10.4067/S0716-09172016000400005Keywords:
Sequence of functions, operational techniques, generating functions, finite summation formulae, Srivastava’s theorem, Singhal Srivastava generating function and Srivastava-Lavoie theorem, secuencia de funciones, Teorema de SrivastavaAbstract
In this paper, authors established various properties of a sequence of functions {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.References
[1] Buchholz, H., The Confluent Hypergeometric Function, SpringerVerlag, New York, (1969).
[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).
[3] McBride, E. B., Obtaining Generating Functions, Springer Verlag, Berlin, (1971).
[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).
[5] Riordan, J., Combinatorial Identities, John Wiley & Sons, Inc., U.S.A., (1968).
[6] Shukla, A. K. and Prajapati, J. C., Some Properties of a Class of Polynomials Suggested by Mittal, Proyecciones Journal of Mathematics, 26(2), pp. 145-156, (2007).
[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).
[8] Srivastava, H. M., Some Generalizations of Carlitz’s Theorem. Pacific J. of Math., 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).
[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).
[11] Srivastava, H. M. and Lavoie, J.-L., A Certain Method of Obtaining Bilateral Generating Functions, Indag. Math., 78(4), pp. 304-320, (1975).
[12] Srivastava, H. M. and Manocha, H. L., A Treatise on Generating Functions, Ellis Harwood Limited-John Wiley and Sons, New York, (1984).
[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).
[3] McBride, E. B., Obtaining Generating Functions, Springer Verlag, Berlin, (1971).
[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).
[5] Riordan, J., Combinatorial Identities, John Wiley & Sons, Inc., U.S.A., (1968).
[6] Shukla, A. K. and Prajapati, J. C., Some Properties of a Class of Polynomials Suggested by Mittal, Proyecciones Journal of Mathematics, 26(2), pp. 145-156, (2007).
[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).
[8] Srivastava, H. M., Some Generalizations of Carlitz’s Theorem. Pacific J. of Math., 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).
[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).
[11] Srivastava, H. M. and Lavoie, J.-L., A Certain Method of Obtaining Bilateral Generating Functions, Indag. Math., 78(4), pp. 304-320, (1975).
[12] Srivastava, H. M. and Manocha, H. L., A Treatise on Generating Functions, Ellis Harwood Limited-John Wiley and Sons, New York, (1984).
Published
2017-03-23
How to Cite
[1]
N. K. Ajudia and J. C. Prajapati, “On a sequence of functions Vn (α,β,δ) (x;a, k, s)”, Proyecciones (Antofagasta, On line), vol. 35, no. 4, pp. 417-436, Mar. 2017.
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