International Journal of Number TheoryLi X-J. On the explicit formula related to Riemann's zeta-function. Int J Number Theory, in press, 2015Li, X-J (2015) On the explicit formula related to Riemann’s zeta-function. Int J Number Theory, in press.
Aside from linear functions, explict functions are expressed in other forms. A quadratic function is explict when it is written in its standard form {eq}y = ax^2 + bx + c {/eq}. An example of this function is {eq}y = 3x^2 - 4x + 10 {/eq} The arithmetic sequence formula can ...
Zeta-functionRitz methodexplicit formulaThis chapter discusses the approach to the superzeta functions (introduced in the previous chapter) by means of Explicit Formulae . In number theory, Explicit Formulae designate certain summation formulae connecting the primes and the Riemann zeros [55, Chap. ...
The terms of order (h2) cancel out because they have opposite sign, thus giving a formula of higher accuracy. It can be seen by writing Eq. (7.28) in the form: (7.29)yi+1=yi+h2f(ti,yi)+h2f(ti+1,yi+1)+O(h3) that this method uses the weighted trajectories of the function y...
We have therefore derived the correct formulae and present them below in a form which is as close as possible to the original format in MOTECC. We list all the formulae for completeness and convenience and the differences between our formulae and the originals are marked by `change bars' ...
In an explicit function, one variable is defined completely in terms of the other. The general form is:y = f(x), for a < x < b
We solve the N-body Calogero problem, \\ie N particles in 1 dimension subjectto a two-body interaction of the form $\\half \\sum_{i,j}[ (x_i - x_j)^2 + g/{(x_i - x_j)^2}]$, by constructing annihilation and creation operators of theform $ a_i^\\mp =\\frac 1 {\...
. The same was done in the deduction of the Gamma-limit for a flat initial configuration in [33] (we notice that another form of the Cosserat curvature energy was considered) and no explicit form of the homogenised curvature energy could be given. In [40], we have announced the form of...
The reason – he felt – was that many of these were clever enough to memorise formula and equations they did not really understand and while this was enough to get them the very highest grades at the lower qualification it made taking the step up extremely challenging because they had little...
From the series expansion of the probability density function we deduce the corresponding expansions of the European call and put option prices. Moreover we deduce closed form formulae for the moments of the forward prices/rates variable. The moment formulae obtained do not involve integrals or ...