Pré-Publication, Document De Travail Année : 2020

Expansions of the Jacobi Theta Functions and Complete Monotonicity Properties

Résumé

In this paper we provide trigonometric expansions and innite products for the theta functions θ j (u, τ), j = 1, 2, 3, 4. This allows us to highlight some complete monotonicity properties for log θ j (u,iπt) θ j (0,iπt) , j = 2, 3, 4 and log θ 1 (u,iπt) θ 1 (0,iπt) as functions with respect to t > 0. We also interested in the quotients S j (u, v, t) = θ j (u 2 ,iπt) θ j (u 2 ,iπt). Some others functions related to θ j will be considered.

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hal-02564413 , version 1 (05-05-2020)
hal-02564413 , version 2 (20-05-2020)

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  • HAL Id : hal-02564413 , version 2

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Abd Raouf Chouikha. Expansions of the Jacobi Theta Functions and Complete Monotonicity Properties. 2020. ⟨hal-02564413v2⟩
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