AN EXTENSION OF POISSON APPROXIMATION BY $w$-FUNCTIONS

APPROXIMATION OF 3D-PARAMETRIC FUNCTIONS BY BICUBIC B-SPLINE FUNCTIONS

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

Poisson Approximation for Unbounded Functions, I: Independent Summands

Let $X_{n1},\cdots,X_{nn},\ n\geq1$, be independent random variables with $P(X_{ni}=1)=1-P(X_{ni}=0)=p_{ni}$ such that $\max\{p_{ni}\colon1\leq i\leq n\}\to0$ as $n\to\infty$. Let $W_n=\sum_{1\leq k\leq n}X_{nk}$ and let $Z$ be a Poisson random variable with mean $\lambda=EW_n$. We obtain an absolute constant bound on $P(W_n=r)/P(Z=r),\ r=0,1,\cdots$, and using this, prove two Poisson approxima...

On Padé Approximation of Some Practical Functions

Approximation of Analytic Functions by Chebyshev Functions

and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...

Approximation of Analytic Functions by Special Functions

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.