Zeros of the Exceptional Laguerre and Jacobi Polynomials

Figure 3

J2: distributions of the zeros 𝜂^{𝑘(ℓ,𝑛)},𝜂^{𝑗(ℓ,𝑛)} (♦), 𝜉^𝑘(ℓ) (○), and 𝜉^𝑘(ℓ) (■) for the J2 Jacobi polynomials, with 𝑔=3,ℎ=4, and ℓ=3. The three diagrams correspond to 𝑛=1(a), 2(b), and 5(c), respectively. The ordinary zeros 𝜂^{𝑗(ℓ,𝑛)} lie in (−1,1).

(a)

(b)

(c)