A new class of functions of bounded index

Shah, S. M.; Shah, S. N.

doi:10.1090/S0002-9947-1972-0313506-8

A new class of functions of bounded index
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by S. M. Shah and S. N. Shah PDF

Trans. Amer. Math. Soc. 173 (1972), 363-377 Request permission

Abstract:

Entire functions of strongly bounded index have been defined and it is shown that functions of genus zero and having all negative zeros satisfying a one sided growth condition belong to this class.

References

Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627

Examples in infinite series with solutions

Fred Gross, Entire functions of bounded index, Proc. Amer. Math. Soc. 18 (1967), 974–980. MR 218564, DOI 10.1090/S0002-9939-1967-0218564-0

Inequalities

Boo-sang Lee and S. M. Shah, On the growth of entire functions of bounded index, Indiana Univ. Math. J. 20 (1970/71), 81–87. MR 259124, DOI 10.1512/iumj.1970.20.20006
Benjamin Lepson, Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., La Jolla, Calif., 1966) Amer. Math. Soc., Providence, R.I., 1968, pp. 298–307. MR 0237788
W. J. Pugh and S. M. Shah, On the growth of entire functions of bounded index, Pacific J. Math. 33 (1970), 191–201. MR 259125, DOI 10.2140/pjm.1970.33.191
S. M. Shah, Entire functions of bounded index, Proc. Amer. Math. Soc. 19 (1968), 1017–1022. MR 237789, DOI 10.1090/S0002-9939-1968-0237789-2
S. M. Shah, Entire functions satisfying a linear differential equation, J. Math. Mech. 18 (1968/1969), 131–136. MR 0227410, DOI 10.1512/iumj.1969.18.18013
S. M. Shah, On entire functions of bounded index whose derivatives are of unbounded index, J. London Math. Soc. (2) 4 (1971), 127–139. MR 322171, DOI 10.1112/jlms/s2-4.1.127