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A note on hypergeometric polynomials

Published online by Cambridge University Press:  17 February 2009

M. I. Qureshi  and
M. A. Pathan
M. A. Pathan
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh-202 001, India.
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Abstract

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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
Information
The ANZIAM Journal , Volume 26 , Issue 2 , October 1984 , pp. 176 - 182
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), 1–11.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), 237–240.CrossRefGoogle Scholar
[4]Carlitz, L., ‘A note on the Laguerre polynomials”, Michigan Math. J. 7 (1960), 219–223.CrossRefGoogle Scholar
[5]Halim, N. A. and Al-Salam, W. A., “Double Euler transformations of certain hypergeometric functions”, Duke Math. J. 30 (1963), 51–62.Google Scholar
[6]Manocha, H. L. and Sharma, B. L., “Summation of infinite series”, J. Austral. Math. Soc. 6 (1966), 470–476.CrossRefGoogle Scholar
[7]Manocha, H. L. and Sharma, B. L., “Some formulae by means of fractional derivatives”, Compositio Math. 18(3) (1967), 229–234.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 + pp′ p″/1q′ q″ + …”, J. Reine Angew. Math. 87 (1879), 26–73.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), 104–114.CrossRefGoogle Scholar