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On relations among some constants of an entire function

1963
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Proceedings of the American Mathematical Society
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+" 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)

doi:10.1090/s0002-9939-1963-0148918-9
fatcat:6gkf46tjnvbuthenxvry5htbqe