On a generalization of some Shah equation

A Dirichlet series ()=+Sigma=2 infinity with the exponents 0<<up arrow+infinity and the abscissa of absolute convergence []>= 0 is said to be pseudostarlike of order is an element of[0,) and type is an element of(0,1] in Pi 0={:Re<0} if '()()-|<|'()()-(2-)|for all is an element of Pi 0. Similarly, the function F is said to be pseudoconvex of order is an element of[0,) and type is an element of(0,1] if divided by F '(s)-h divided by divided by divided by0 in Pi 0. Conditions on parameters 1,2,1,2,1,2, under which the differential equationdnwdsn +(1+2)+(1+2)=1+2,>= 2,has an entire solution pseudostarlike or pseudoconvex of order is an element of[0,) and type is an element of(0,1], or close-to-pseudoconvex in Pi 0 Pi 0 are found. It is proved that for such solution lnM(sigma,F)=(1+o(1))nn root|b1|heh sigma/nas sigma ->+infinity,ln(,)=(1+(1))|1|/as ->+infinity,where M(sigma,F)=sup{|F(sigma+it)|:t is an element of R}(,)=sup{|(+)|:is an element of}.