ONLY FOUR EULER INFINITY PRODUCTS ARE THETA-TYPE FUNCTIONS
Résumé
This paper follows our previous work [14]. A function is called theta-type when its asymptotic behavior near any root of unity is similar like as what happened for any Jacobi theta function. It will be shown that only four Euler infinite products have this property. This will be obtained by investigating the analyticity obstacle of a Laplace-type integral of the exponential generating function of Bernoulli numbers.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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