Vol. 24, No. 2, 1968

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On the derivative of canonical products

Morris Marden

Vol. 24 (1968), No. 2, 331–339
Abstract

In this paper we study an entire function of genus p that has the canonical product form

      ∞∏               [                2
f(z) =  [1− (z∕aj)]exp (z∕aj)+ (1∕2)(z∕aj) + ⋅⋅⋅
j=1
+ (1∕p)(z∕aj)p].
For the derivative fof such a function we develop some results analogous to the theorems of Lucas and Jensen for polynomials, as well as some results in the case that all but one aj lie on a prescribed set.

Mathematical Subject Classification
Primary: 30.55
Milestones
Received: 22 June 1967
Published: 1 February 1968
Authors
Morris Marden