electrostatic interpretation

(0.001 seconds)

3 matching pages

1: 31.15 Stieltjes Polynomials
This is the Stieltjes electrostatic interpretation. …
2: 29.12 Definitions
29.12.13 ${\frac{\rho+\frac{1}{4}}{\xi_{p}}+\frac{\sigma+\frac{1}{4}}{\xi_{p}-1}+\frac{% \tau+\frac{1}{4}}{\xi_{p}-k^{-2}}+\sum_{\begin{subarray}{c}q=1\\ q\neq p\end{subarray}}^{n}\frac{1}{\xi_{p}-\xi_{q}}=0},$ $p=1,2,\dots,n$.
This result admits the following electrostatic interpretation: Given three point masses fixed at $t=0$, $t=1$, and $t=k^{-2}$ with positive charges $\rho+\tfrac{1}{4}$, $\sigma+\tfrac{1}{4}$, and $\tau+\tfrac{1}{4}$, respectively, and $n$ movable point masses at $t_{1},t_{2},\dots,t_{n}$ arranged according to (29.12.12) with unit positive charges, the equilibrium position is attained when $t_{j}=\xi_{j}$ for $j=1,2,\dots,n$.
3: 18.39 Physical Applications
For interpretations of zeros of classical OP’s as equilibrium positions of charges in electrostatic problems (assuming logarithmic interaction), see Ismail (2000a, b).