Zeros of the Exceptional Laguerre and Jacobi Polynomials

Figure 1

L1: distributions of the zeros 𝜂^{𝑘(ℓ,𝑛)},𝜂^{𝑗(ℓ,𝑛)} (♦), 𝜉^𝑘(ℓ) (○), and 𝜉^𝑘(ℓ) (■) for the L1 Laguerre polynomials, with 𝑔=0.5 and ℓ=2. The three diagrams correspond to 𝑛=1(a), 2(b), and 3(c), respectively. The ordinary zeros 𝜂^{𝑗(ℓ,𝑛)} lie in (0,∞).

(a)

(b)

(c)