Equivalence of the logarithms of the maximum modulus and the maximum term of an entire series of Dirichlet

1987 ◽  
Vol 42 (2) ◽  
pp. 624-630
Author(s):  
M. N. Sheremeta
Keyword(s):  
Maximum Modulus ◽  
Maximum Term ◽  
Entire Series

VI.—The Maximum Term of an Entire Series

1953 ◽  
Vol 64 (1) ◽  
pp. 80-89
Author(s):  
S. M. Shah ◽  
S. K. Singh
Keyword(s):  
Entire Function ◽  
Infinite Order ◽  
Maximum Modulus ◽  
Zero Order ◽  
Maximum Term ◽  
Entire Series

SynopsisThe relation between the maximum term and the maximum modulus of an entire function is exhibited by means of general theorems and specific examples. Functions of zero order and of infinite order are mainly considered.

scholarly journals Growth Estimates of Composite Entire Functions in the Light of Slowly Changing Functions Based Relative Order, Relative Type and Relative Weak Type

2015 ◽  
Vol 54 (1) ◽  
pp. 59-74
Author(s):  
S. K. Datta ◽  
T. Biswas ◽  
S. Bhattacharyya
Keyword(s):  
Weak Type ◽  
Entire Functions ◽  
Maximum Modulus ◽  
Relative Order ◽  
Maximum Term ◽  
Growth Properties ◽  
Relative Type

Abstract In the paper we prove some growth properties of maximum term and maximum modulus of composition of entire functions on the basis of relative L*-order, relative L*-type and relative L*-weak type.

The Maximum Term and the Rank of an Entire Function

1969 ◽  
Vol 21 ◽  
pp. 257-261
Author(s):  
V. Sreenivasulu
Keyword(s):  
Entire Function ◽  
Maximum Modulus ◽  
Maximum Term ◽  
Proximate Order ◽  
Image Position

1. For an entire function , let M(r, f), μ(r, f), and v(r, f) denote the maximum modulus, the maximum term, and the rank for |z\ = r, respectively. Also, letand λ(r) the lower proximate order relative to log M(r, f). For the properties of the lower proximate order, we refer the reader to the paper by Shah (1).2. We prove the following theorems.THEOREM 1. For an entire functionwhere μ(r, f1) and M(r, f1) correspond to fl(z), the derivative of f(z), provided (n + l)Rn > nRn+1, when L(f) > 1.

scholarly journals On the maximum modulus and maximum term of composition of entire functions

2004 ◽  
Vol 35 (4) ◽  
pp. 293-300
Author(s):  
S. K. Vaish ◽  
R. Chankanyal
Keyword(s):  
Entire Functions ◽  
Maximum Modulus ◽  
Maximum Term ◽  
Growth Properties ◽  
Left And Right

We study some growth properties of maximum modulus and maximum term of composition of entire functions of $(p,q)$-order as compared to the growth of their corresponding left and right factors. Some of the results that we obtain here generalize and improve the known results of Singh and Baloria, and, Song and Yang.

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