A note on an analogue of Hadamard's theorem for determining the radii of m-meromorphy

Nattapong Bosuwan

ABSTRACT: In this paper, we prove an extension of Hadamard?s classical theorem for determining the radius of mmeromorphy of an analytic function in terms of its Taylor coefficients. Our extension is expressed in terms of Fourier coefficients with respect to an orthonormal polynomial system on the unit circle. Our main result confirms a conjecture posed in [Dolomit Res Notes Approx 17 (2024):12?21].

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^a	Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400 Thailand
^b	Centre of Excellence in Mathematics, CHE, Bangkok 10400 Thailand

* Corresponding author, E-mail: nattapong.bos@mahidol.ac.th

Received 7 Mar 2024, Accepted 5 Oct 2024