Mathematics – Analysis of PDEs
Scientific paper
2010-08-30
Mathematics
Analysis of PDEs
28 pages
Scientific paper
We establish the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, including the mapping relations between power series and trigonometric series, and by using such mapping relations we obtain a general method to find the sum function of a trigonometric series. According to this method, if each coefficient of a power series is respectively equal to that of a trigonometric series, then if we know the sum function of the power series, we can obtain that of the trigonometric series, and the non-analytical points of which are also determined at the same time, thus we obtain a general method to find the sum of the Dirichlet series of integer variables, and derive several new properties of $\zeta(2n+1)$.
Bi Guangqing
Bi Yuekai
No associations
LandOfFree
New Properties of Fourier Series and Riemann Zeta Function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with New Properties of Fourier Series and Riemann Zeta Function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Properties of Fourier Series and Riemann Zeta Function will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-400739