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ASYMPTOTIC EXPANSIONS OF ZEROS OF A PARTIAL THETA FUNCTION

Abstract : The bivariate series θ(q, x) := ∞ j=0 q j(j+1)/2 x j defines a partial theta function. For fixed q (|q| < 1), θ(q, .) is an entire function. We prove a property of stabilization of the coefficients of the Laurent series in q of the zeros of θ. The coefficients r k of the stabilized series are positive integers. They are the elements of a known increasing sequence satisfying the recurrence relation r k = ∞ ν=1 (−1) ν−1 (2ν + 1)r k−ν(ν+1)/2 .
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https://hal.archives-ouvertes.fr/hal-01291208
Contributor : Vladimir Kostov <>
Submitted on : Monday, March 21, 2016 - 4:42:45 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM

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Vladimir Kostov. ASYMPTOTIC EXPANSIONS OF ZEROS OF A PARTIAL THETA FUNCTION. Comptes rendus de l'Académie bulgare des Sciences, Bulgarian Academy of Sciences, 2015. ⟨hal-01291208⟩

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