In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.  

Let s ? 3 $s \geqslant 3$ be a natural number, let ? ( x ) $\psi (x)$ polynomial with real coefficients and degree d 2 $d 2$ , A $A$ some large, non-empty, finite subset of numbers. We use E $E_{s,2}(A)$ to denote the number solutions system equations ? i = 1 ? + 0 \begin{equation*}\hskip2.5pc \sum _{i=1}^{s} (\psi (x_i) - \psi (x_{i+s}) )= (x_i x_{i+s} 0, \end{equation*} where ? $x_i \in A$ fo...

The cumulative distribution function of the non-central chi-square χn′2(λ) n degrees freedom possesses an integral representation. Here we rewrite this in terms a lower incomplete gamma applying two second mean-value theorems for definite integrals, which are Bonnet type and Okamura’s variant du Bois–Reymond theorem. Related results exposed concerning small argument cases (CDF) their asymptotic...