Most of the classical results on the zeros of the polynomial will now be extended to power series. In particular, power series convergent in a disk satisfy a Schwarz Lemma that is even simpler than in . We will also notice Dieudonne-Dwork's Theorem#In this chapter,ris a strictly positive ...
Most of classical results on zeros of polynomials will now be extended to power series. In particular, power series converging inside a disk satisfy a Schwarz Lemma that is even simpler than in .#Throughout this chapter,ris a strictly positive real number andr′,r″ are strictly positive real...
For a power series which converges in some neighborhood of the origin in the complex plane, it turns out that the zeros of its partial sums---its sections---often behave in a controlled manner, producing intricate patterns as they converge and disperse. We open this thesis with an overview...
We are concerned with zeros of random power series with coefficients being a stationary, centered, complex Gaussian process. We show that the expected number of zeros in every smooth domain in the disk of convergence is less than that of the hyperbolic Gaussian analytic function with i.i.d. ...
Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate distribution at zero, with a mixing probability $p$ for the ...
A typical example of GAF is provided by the i.i.d. Gaussian power series defined on the unit disk: Letandbe i.i.d. standard complex Gaussian random variables with densityand consider a random power series, (1.1) which defines an analytic function ona.s. This gives a GAF onwith a cova...
[25] One way of describingthis theoretical wall is in terms of a power series in photon momentum. (modulo the Q/p · q factor). The zerothand first order terms are controlled by translation and Lorentz symmetry, respectively. The isolated instance ofsecond-order terms in the Yang-Mills ...
as a power series around k = 0, whereas the second is obtained using integration by partsd(k) =b a d(x)e ikx dx = 1 ikd(b)e ikb −d(a)e ika相关精品文档 更多 Multivariate Probability Distributions 3.1 Quadratic Functions and Models Section 3.2 Investigating Quadratic Functions...
On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions The general theories of the derivation of inverses of functions from their power series and asymptotic expansions are discussed and compared. The asymptoti... BR Fabijonas,FWJ Olver - 《Siam Review》 被引量: 33发...
We will also need the power seriess(4) HX) = r^fv(X) = £ ^ram+v)gm+v-^sWs^ Ws^ o 4mm\Y{v+m+\)sand the inequality [9, =-=(5)-=-1s(5) /„, > max(/Vi,|H)> - 1 0, 0 < x < 5.s(The second assertion is a consequence of the first and of (1), or ...