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1: 31.15 Stieltjes Polynomials
This is the Stieltjes electrostatic interpretation. …
2: 29.12 Definitions
29.12.13 ρ + 1 4 ξ p + σ + 1 4 ξ p - 1 + τ + 1 4 ξ p - k - 2 + q = 1 q p n 1 ξ p - ξ q = 0 , p = 1 , 2 , , 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 ρ + 1 4 , σ + 1 4 , and τ + 1 4 , respectively, and n movable point masses at t 1 , t 2 , , t n arranged according to (29.12.12) with unit positive charges, the equilibrium position is attained when t j = ξ j for j = 1 , 2 , , 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).