Rapidly Converging Series forζ(2n+1)from Fourier Series
نویسندگان
چکیده
منابع مشابه
SOME RAPIDLY CONVERGING SERIES FOR ζ(2n + 1)
For a natural number n, the author derives several families of series representations for the Riemann Zeta function ζ(2n + 1). Each of these series representing ζ(2n + 1) converges remarkably rapidly with its general term having the order estimate: O(k−2n−1 ·m−2k) (k →∞; m = 2, 3, 4, 6). Relevant connections of the results presented here with many other known series representations for ζ(2n + 1...
متن کاملRapidly-Converging Series Representations of aMutual-Information Integral
This paper evaluates a mutual-information integral that appears in EXIT-chart analysis and the capacity equation for the binaryinput AWGN channel. Rapidly-converging series representations are derived and shown to be computationally efficient. Over a wide range of channel signal-to-noise ratios, the series are more accurate than the Gauss-Hermite quadrature and comparable to Monte Carlo integra...
متن کاملDetermination of a jump by Fourier and Fourier-Chebyshev series
By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation. This is achieved without the finiteness assumption on the number of discontinuities. Two results on determination of ...
متن کاملFourier Series
for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...
متن کاملFourier Series
Here are some facts about Fourier Series — useful for pde and elsewhere. Proofs of Lemmas are easy exercises, and not given. On the other hand, proofs of LEMMAS are harder; their proofs are indicated, or a reference is given.
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: Abstract and Applied Analysis
سال: 2014
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2014/457620