On entire functions of fast growth

Abstract

ABSTRACT. Let (*) A*) = V"z " n=0 be a transcendental entire function. Set Ai(r) = max \fiz)\, m(r) = max {la \r "} \z\=r n>0and N(r) = max {XJm(r) = \a"\r "}. For the case q = 2, these notions are due to Whittakar and Shah respectively.

On Entire Functions of Fast Growth

“…It will be seen that the results which we obtain generalize and improve considerably the results contained in [1] (ii) hminf1Ogtrll0(jC) =a (0<a<oo).…”

Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

“…For the first shortcoming, there were some concepts such as logarithmic order, h-order, and generalize order (see [21][22][23][24]). However, to cover these shortcomings simultaneously, the concepts of (p, q)-order and (p, q)-type were good ideas and were used to estimate the growth of a class of entire functions represented by LaplaceStieltjes transforms more precisely, which were given by Juneja, Kapor, and Bajpai [25][26][27].…”

Approximation of Entire Functions of Slow Growth

“…Many researches have done in-depth research and many important results, which have been obtained in [1−8] . For example, S. M. Shah [1] and S. K. Bajpai [2] gave some different characterizations on the coefficients and the maximum modulus, the maximum term, and the rank of the maximum term for the Taylor entire function of fast growth ρ = ∞. On the other hand, G. P. Kapoor, A. Nautiyal [3−4] and R. Ganti, G. S. Srivastava [5] continued this work and defined generalized order and generalized type for the Taylor entire function of slow growth ρ = 0 in a new way, as follows:…”