Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-23T22:05:22.819Z Has data issue: false hasContentIssue false

A note on hypergeometric polynomials

Published online by Cambridge University Press:  17 February 2009

M. A. Pathan
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh-202 001, India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a paper which appeared in this journal, Manocha and Sharma [6] obtained some results of Carlitz [4], Halim and Salain [5] and generalized a few of them by using fractional derivatives. The present paper is concerned with some erroneous results of this paper [6]. Many more sums of the product of hypergeometric polynomials are also obtained.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Abiodun, R. F. A., “Transformation formulae for Kampé de Fénet function”, Nederl. Akad. Wetensch. Proc. Ser. A 83 (1980), 111.CrossRefGoogle Scholar
[2]Bailey, W. N., Generalized hypergeometric series (Cambridge University Press, London, 1935).Google Scholar
[3]Bailey, W. N., “On the sum of a terminating 3 F3(l)”, Quart. J. Math. Oxford Ser. (2) 4 (1953), 237240.CrossRefGoogle Scholar
[4]Carlitz, L., ‘A note on the Laguerre polynomials”, Michigan Math. J. 7 (1960), 219223.CrossRefGoogle Scholar
[5]Halim, N. A. and Al-Salam, W. A., “Double Euler transformations of certain hypergeometric functions”, Duke Math. J. 30 (1963), 5162.Google Scholar
[6]Manocha, H. L. and Sharma, B. L., “Summation of infinite series”, J. Austral. Math. Soc. 6 (1966), 470476.CrossRefGoogle Scholar
[7]Manocha, H. L. and Sharma, B. L., “Some formulae by means of fractional derivatives”, Compositio Math. 18(3) (1967), 229234.Google Scholar
[8]Rainville, E. D., Special functions (Macmillan, New York, 1960).Google Scholar
[9]Thomas, J., “Üeber die Funktionen welche durch Reihen von der Form dargestellt werden, 1 + ppp″/1qq″ + …”, J. Reine Angew. Math. 87 (1879), 2673.Google Scholar
[10]Whipple, F. J. W., “A group of generalized hypergeometric series relations between 120 allied series of the type F[a, b, c; d, e]”, Proc. London Math. Soc. (2) 23 (1925), 104114.CrossRefGoogle Scholar