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B.K. Singh1
Section:Research Paper, Product Type: Journal-Paper
Vol.7 ,
Issue.3 , pp.93-102, Jun-2020
Online published on Jun 30, 2020
Copyright © B.K. Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: B.K. Singh, “Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.3, pp.93-102, 2020.
MLA Style Citation: B.K. Singh "Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n." International Journal of Scientific Research in Mathematical and Statistical Sciences 7.3 (2020): 93-102.
APA Style Citation: B.K. Singh, (2020). Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n. International Journal of Scientific Research in Mathematical and Statistical Sciences, 7(3), 93-102.
BibTex Style Citation:
@article{Singh_2020,
author = {B.K. Singh},
title = {Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {6 2020},
volume = {7},
Issue = {3},
month = {6},
year = {2020},
issn = {2347-2693},
pages = {93-102},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1941},
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1941
TI - Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - B.K. Singh
PY - 2020
DA - 2020/06/30
PB - IJCSE, Indore, INDIA
SP - 93-102
IS - 3
VL - 7
SN - 2347-2693
ER -
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Abstract :
In this paper, we study the asymptotic behaviours of generalized hypergeometric polynomial Set Sn(x,y) for large value of n, the order of the polynomial sets. Generating function is generally used for the determination of the asymptotic behaviours of the polynomial set as the order of the polynomial set tends to infinity. Hence if the radius of convergence is finite, then the generating function has one or several singularities on the circle of convergence and the location and nature of these singularities determine the behaviours of the polynomial set when the order tends to infinity, But here we have obtained the asymptotic behaviours not from the generating function but by another method directly from the polynomial set. These behaviours for large n have been given in the form of Theorem. A number of well known results for orthogonal and non-orthogonal polynomials have been deduced as particular cases of these theorems.
Key-Words / Index Term :
Appell function, Hypergeometric polynomial, Orthogonal polynomial, Generating function, Asymptotic Behaviours
References :
[1] Sanjay Kr. Suman and Brijendra Kr. Singh ?An Effort towards the generalized hypergeometric Polynomials of two variables? Research Guru online Journal Vol. 13, Issue 4, pp.1-11, March 2020 (ISSN: 2349-266X)
[2] P. Appell, and Kampe de Feriet, J. ?Fonctions Hypergeometriques et Hyperspheriques, polynomies d? Hemite, Gauthier-Villars? Paris,1926.
[3] J.L. Burchnall and T.W. Chaundy ?Expansions of Appell`s double Hypergeometric function (II)? Quart. J. Math. Oxford ser, 12, pp.112-128, 1941.
[4] E.D. Rainville Special functions. Mac Millan Co. New York,1960.
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