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A theorem on the growth of entire functions on asymptotic paths and its application to the oscillation theory of $w''+Aw=0$
Let A=A(z) be a transcendental entire function and let w u w 2 be two linearly independent entire solutions of the differential equation ( 1)w"+Aw=0.It is known that any non-zero solution of ( 1) is an entire function of infinite order ([1]).Put It then holds ([1], p. 354) that( 2)where …