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Vanishing coefficients in infinite product expansions

Published online by Cambridge University Press:  09 April 2009

George E. Andrews  and
David M. Bressoud
George E. Andrews
Affiliation:
The Pennsylvania State UniversityUniversity Park Pennsylvania 16802, U.S.A.
David M. Bressoud
Affiliation:
The Pennsylvania State UniversityUniversity Park Pennsylvania 16802, U.S.A.
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Abstract

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Richmond and Szekeres (1977) have conjecturned that certain of the coefficients in the power series expansions of certain infinite products vanish. In this paper, we prove a general family of results of this nature which includes the above conjectures.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 2 , March 1979 , pp. 199 - 202
Copyright
Copyright © Australian Mathematical Society 1979

References

Andrews, G. E. (1969), ‘On Ramanujan's summation of 1ψ1 (a; b; z), Proc. Amer. Math. Soc. 22, 552–553.Google Scholar
Andrews, G. E. (1976), The theory of partitions (Encyclopedia of Math. and its Applications, Vol.2, Addison-Wesley, Reading, Mass.).Google Scholar
Andrews, G. E. and Askey, R. A. (1977), ‘A simple proof of Ramanujan's summation of the 1ψ1 summation’, Aequationes Math. (to appear).Google Scholar
Ismail, M. (1977), ‘A simple proof of Ramanujan's 1ψ1 summation’, Proc. Amer. Math. Soc. 63, 185–186.Google Scholar
Richmond, B. and Szekeres, G. (1977), ‘The Taylor coefficients of certain infinite products’, Acta Szeged (to appear).Google Scholar