We prove a Lipschitz type summation formula with periodic coefficients. Using this formula, representations of the values at positive integers of Dirichlet L-functions with periodic coefficients are obtained in terms of Bernoulli numbers and certain sums involving essentially the discrete Fourier transform...
In that case, the resummation adds to the small divisor iω ·ν a quantity −ε(ω·ν) 2 + Mn(ω·ν;ε), and one can prove that Mn(x,ε) is smooth in x and it is real at x = 0, so that the dressed propag...
{ T}}}\), that is, the derivative ofξto the parameter at phasekof the cycle. In the linear model (8.2), this is given by thekth term in the summation in (8.11). In the case of the nonlinear model (8.36), the derivative is obtained from Eq. (8.46) by setting all blocks of\...
However, simulating a deterministic, yet chaotic system with deterministic finite-precision numbers always results in closed periodic orbits due to a finite set of possible states11. One may think of these orbits asbitwiseperiodic, in the sense that they eventually return to a state in which every...
We prove limit laws for infinite horizon planar periodic Lorentz gases when, as timentends to infinity, the scatterer sizemay also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the disp...
,(im,i1,⟨gm⟩)⟩ must have ∑igi=0, and the summation of the values of gi for all paths in a positive periodic graph is positive. We know that a positive periodic graph does not contain a cycle. Definition 6 (Weight-Transit Periodic Graph) Let G=(V,E,w) be a static ...
C.W. Clenshaw A note on the summation of Chebyshev series Math. Tab. Wash. (1955) S. Coffey et al. Compression of satellite orbits Adv. Astronaut. Sci. (1996)View more references Cited by (1) Algorithms for the integration and derivation of Chebyshev series 2004, Applied Mathematics and ...
convergesabsolutelyinthehalf-plane{s∈C:(s)>1}.Aneasypartialsummationargu- mentshowsthattheseries(1.2)convergesconditionallyinthehalf-plane{s∈C:(s)>0} ifandonlyifM(g)=0. Henceforth,weshalldenotetheabscissaofconvergenceoftheDirichletseries(1.2)by σ g .Thatis, σ g :=inf{σ∈R:(1.2)conver...
Now we “lift” a∈ l2 to L2(0, π) by the summation (3) Clearly, the nth Fourier coefficient of f(t) is expressed as (4) We define the backward shift acting on L2(0, π) as (5) Therefore (6) Our main result is the following. Theorem 1. can be expressed as (7...
5. O. Costin, On Borel summation and Stokes phenomena for rank one nonlinear systems of ODE's, Duke Math. J. 93:289–344 (1998). O. Costin, R. D. Costin, and J. Lebowitz, Transition to the continuum of a particle in time-periodic potentials, in Advances in Differential Equations an...