On relations among some constants of an entire function

J. Gopala Krishna
1963 Proceedings of the American Mathematical Society  
+" inf M = Mip,f) sup for lim x-p I ft)/tdl. X-»+ CO J i m = mip,f) inf If Piz) is an entire function of order p, it is known that (1) M, m are its type and co-type, in case/ happens to be the rank (or position) function of the maximum term of the Maclaurin series of P (see Chapter II of [l] and Chapter II of [2]) and that (2) M and m are the logarithmic type and co-type of P, if fix) is the number of zeroes z of Piz) such that \z\ ^x (see Jensen's Theorem, Chapter III of [2])-Also let (pit)
more » ... )-Also let (pit) and xfrit) stand for the extended real valued strictly decreasing and continuous functions over the closed (0, 1), defined by the equations (see Lemmas I and II of [3]) (1 -it) = t, (1 + 4,(t)) expi-m) = t. C. R. Rao, improving upon a number of results known earlier, has shown (see [3] and its corrigendum), Received by the editors May 2, 1962.
doi:10.1090/s0002-9939-1963-0148918-9 fatcat:6gkf46tjnvbuthenxvry5htbqe