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The difference operators and extended Laguerre polynomials

Published online by Cambridge University Press:  17 April 2009

B.P. Parashar
B.P. Parashar
Affiliation:
Department of Mathematics, Rani Durgawati Vishwa Vidyalaya, Jabalpur (M.P.), India.
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Abstract

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A new set of polynomials in powers of xh (h > 0) which are related to the Laguerre polynomials , have been defined by a Rodrigues type formula involving the forward difference operator Δh of increment h. Besides obtaining shift operator formulae for , a definition of fractional power of Δh has been given. The definition has been illustrated by establishing known relations of the confluent hypergeometric function.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 111 - 119
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Erdelyi, Arthur, Magnus, Wilhelm, Oberhettinger, Fritz, Tricomi, Francesco G. (edited by), Higher transcendental functions, Volume II (Based, in part, on notes left by Harry Bateman. McGraw-Hill, New York, Toronto, London, 1953).Google Scholar
[2]Erdélyi, Arthur, Magnus, Wilhelm, Oberhettinger, Fritz, Tricomi, Francesco G. (edited by), Higher transcendental functions, Volume III (Based, in part, on notes left by Harry Bateman. McGraw-Hill, New York, Toronto, London, 1955).Google Scholar
[3]Jordan, Charles, Calculus of finite differences, 2nd edition (Chelsea, New York, 1960).Google Scholar
[4]Konhauser, Joseph D.E., “Biorthogonal polynomials, suggested by the Laguerre polynomials”, Pacific J. Math. 21 (1967), 303–314.CrossRefGoogle Scholar
[5]Slater, L.J., Confluent hypergeometric functions (Cambridge University Press, Cambridge, 1960).Google Scholar
[6]Toscano, Letterio, “Operatori differenzialie polinomi di Laguerre”, Matematiche (Catania) 23 (1968), 197–223.Google Scholar
[7]Tricomi, Francesco G., Vorlesungen über Orthogonalreihen (Die Grundlehren der mathematischen Wissenschaften, 76. Springer-Verlag, Berlin, Gottingen, Heidelberg, 1955).CrossRefGoogle Scholar