Analytic continuation of generalized trigonometric functions
نویسندگان
چکیده
Via a unified geometric approach, class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they univalent. Some consequences deduced concerning radius convergence for the Maclaurin series, commutation rotation, continuation beyond domain univalence, and periodicity.
منابع مشابه
Generalized Trigonometric Functions: 10744
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...
متن کاملAnalytic continuation of multiple Hurwitz zeta functions
We use a variant of a method of Goncharov, Kontsevich, and Zhao [Go2, Z] to meromorphically continue the multiple Hurwitz zeta function ζd(s; θ) = ∑ 0<n1<···<nd (n1 + θ1) −s1 · · · (nd + θd)d , θk ∈ [0, 1), to C, to locate the hyperplanes containing its possible poles, and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s; θ).
متن کاملAnalytic Continuation of Multiple Zeta Functions
In this paper we shall define the analytic continuation of the multiple (Euler-Riemann-Zagier) zeta functions of depth d: ζ(s1, . . . , sd) := ∑ 0 1 and ∑d j=1 Re (sj) > d. We shall also study their behavior near the poles and pose some open problems concerning their zeros and functional equations at the end.
متن کاملConvoluted Generalized White Noise, Schwinger Functions and Their Analytic Continuation to Wightman Functions
We construct Euclidean random fields X over IR, by convoluting generalized white noise F with some integral kernels G, as X = G ∗ F . We study properties of Schwinger (or moment) functions of X. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Schwinger functions which we then apply to the above fields. We present a partial negative result on...
متن کاملInequalities involving generalized trigonometric and hyperbolic functions
The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2022
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/bproc/119