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Existence theorem for proximate type of entire functions with index-pair (p, q)
Published online by Cambridge University Press: 17 April 2009
Abstract
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R.S.L. Srivastava and O.P. Juneja (1967) proved an existence theorem for the proximate type T (r) of an entire function with classical growth. For an interesting generalization of this theorem for an entire function with index-pair (p,q), which is due essentially to H.S. Kasana and S.K. Vaish (1984), a remarkably simple (and markedly different) construction of T (r) is presented here. The main theorem established here applies to a much larger class of entire functions with index-pair (p,q) than that considered earlier.
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- Copyright © Australian Mathematical Society 1987
References
[1]Juneja, O.P., Kapoor, G.P. and Bajpai, S.K., “On the (p, q)-order and lower (p, q)-order of an entire function”, J. Reine Angew. Math. 282 (1976), 53–67.Google Scholar
[2]Juneja, O.P., Kapoor, G.P. and Bajpai, S.K., “On the (p, q)-type and lower (p, q)-type of an entire function”, J. Reine Angew. Math. 290 (1977), 180–190.Google Scholar
[3]Kasana, H.S. and Vaish, S.K., “On the proximate type and λ-proximate type of an entire function with index-pair (p, q)”, Math. Japon. 29 (1984), 331–339.Google Scholar
[4]Srivastava, R.S.L. and Juneja, O.P., “On proximate type of entire functions”, Compositio Math. 18 (1967), 7–12.Google Scholar
[5]Valiron, G., Lectures on the General Theory of Integral Functions (Translated from the French by Collingwood, E.F.) Chelsea, New York, 1949.Google Scholar
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