ON THE PROXIMATE ORDER OF AN ENTIRE FUNCTION WITH INDEX PAR

Naresh Kumar, G. S. Srivastava
1988 Demonstratio Mathematica  
n iS 1. Let fCzD = V a z , where z = re and is any n=0 sequence of complex numbers, be a non-constant entire function. We set MCrD = max |fCzD|, fKrD = max < |ajr n > |z|=r n20 and vCrD » max < n:/Xr3 = |an|r n >. Then MCrD, and vCr) are called respectively the maximum modulus, the maximum term and the rank of the maximum term of fCz) for |z|sr. It is well known that log MCr3 and log /jCr3 are indefinitely increasing convex function of log r and vCr5 is a nondecreasing integer valued function
more » ... r valued function of r. Further CC8],p.31D iXr3 and pCrD are related by the equation r CI,. 13 log /nCrD = 0C13 + J dx> 0 < rQ< r. r 0 An entire function fCz3 is said to be of order /0C13 if Unauthenticated Download Date | 2/25/20 2:21 AM
doi:10.1515/dema-1988-0102 fatcat:rpigaxgl3fefpiupe4ovbjmv4m