Some new hybrid power mean formulae of trigonometric sums
نویسندگان
چکیده
منابع مشابه
On Some Trigonometric Power Sums
In contrast to Fourier series, these finite power sums are over the angles equally dividing the upper-half plane. Moreover, these beautiful and somewhat surprising sums often arise in analysis. In this note, we extend the above results to the power sums as shown in identities (17), (19), (25), (26), (32), (33), (34), (35), and (36) and in the appendix. The method is based on the generating func...
متن کاملA hybrid mean value involving a new Gauss sums and Dedekind sums
In this paper, we introduce a new sum analogous to Gauss sum, then we use the properties of the classical Gauss sums and analytic method to study the hybrid mean value problem involving this new sums and Dedekind sums, and give an interesting identity for it.
متن کاملSome Notes on Trigonometric Sums
1 Trigonometric Sums 1 1.1 Gauss Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Kloosterman Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Geometrization 2 2.1 A Lemma on Torsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Artin-Shreier Sheaves . . . . . . . . . . . . . . . . . ...
متن کاملBasic Trigonometric Power Sums with Applications
− 2 , where m is a positive integer and subject to m < n + 1 [28]. In this equation ⌊n/2⌋ denotes the floor function of n/2 or the greatest integer less than or equal to n/2. A solution to the above problem was presented shortly after by Greening et al. in [18]. Soon afterwards, there appeared a problem involving powers of the secant proposed by Gardner [15], which was solved partially by Fishe...
متن کاملSymbolic computation of some power-trigonometric series
Let f∗(z) = ∞ ∑ j=0 aj z j be a convergent series in which {aj}j=0 are known real numbers. In this paper, by referring to Osler’s lemma [8], we obtain explicit forms of the two bivariate series ∞ ∑ j=0 an j+m r j cos(α+ j)θ and ∞ ∑ j=0 an j+m r j sin(α+ j)θ, where r, θ are real variables, α ∈ R, n ∈ N and m ∈ {0, 1, . . . , n − 1}. With some illustrative examples, we also show how to obtain the...
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: Advances in Difference Equations
سال: 2020
ISSN: 1687-1847
DOI: 10.1186/s13662-020-02660-7