♦ 7 matching pages ♦
7 matching pages
… ►For physical applications of -Laguerre polynomials see §17.17. ►For interpretations of zeros of classical OP’s as equilibrium positions of charges in electrostatic problems (assuming logarithmic interaction), see Ismail (2000a, b).
An electrostatics model for zeros of general orthogonal polynomials.
Pacific J. Math. 193 (2), pp. 355–369.
More on electrostatic models for zeros of orthogonal polynomials.
Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.
… ►This is the Stieltjes electrostatic interpretation. …
§22.19(v) Other Applications►Numerous other physical or engineering applications involving Jacobian elliptic functions, and their inverses, to problems of classical dynamics, electrostatics, and hydrodynamics appear in Bowman (1953, Chapters VII and VIII) and Lawden (1989, Chapter 5). …
29.12.13 .►This result admits the following electrostatic interpretation: Given three point masses fixed at , , and with positive charges , , and , respectively, and movable point masses at arranged according to (29.12.12) with unit positive charges, the equilibrium position is attained when for .
… ►Laplace’s equation governs problems in heat conduction, in the distribution of potential in an electrostatic field, and in hydrodynamics in the irrotational motion of an incompressible fluid. …
The second Painlevé equation in the electrostatic probe theory: Numerical solutions for the partial absorption of charged particles by the surface.
Technical Physics 49 (1), pp. 1–7.