Zeros of the Exceptional Laguerre and Jacobi Polynomials

Table 1

List of the zeros 𝜉^𝑘(ℓ), 𝜉^𝑘(ℓ), and 𝜂^{𝑘(ℓ,𝑛)} for the L1 Laguerre polynomials with 𝑔=2, ℓ=5, and 𝑛=0,10,20,…,60 (𝑘=1,2,…,ℓ). It can be seen that when 𝑛=0, 𝜂^{𝑘(ℓ,𝑛=0)}=𝜉^𝑘(ℓ). As 𝑛 increases, 𝜂^{𝑘(ℓ,𝑛)} approaches to 𝜉^𝑘(ℓ).

𝜉^𝑘(ℓ):		−22.4802	−15.2391	−10.1403	−6.2977	−3.3427
	𝑛=0	−22.4802	−15.2391	−10.1403	−6.2977	−3.3427
	10	−22.0686	−14.8767	−9.8314	−6.0505	−3.1698
	20	−21.8830	−14.7189	−9.7004	−5.9469	−3.0962
𝜂^𝑘(ℓ,𝑛):	30	−21.7717	−14.6253	−9.6233	−5.8862	−3.0529
	40	−21.6954	−14.5617	−9.5711	−5.8452	−3.0237
	50	−21.6390	−14.5148	−9.5327	−5.8152	−3.0022
	60	−21.5951	−14.4784	−9.5030	−5.7919	−2.9856
𝜉^𝑘(ℓ):		−21.0456	−14.0274	−9.1375	−5.5071	−2.7824