Monotonicity Properties of the Zeros of
β
ΓrpΓ‘d Elbert; Panayiotis D. Siafarikas
π
Article
π
1999
π
Elsevier Science
π
English
β 111 KB
## Let x (*) n, k , k=1, 2, ..., [nΓ2], denote the k th positive zero in increasing order of the ultraspherical polynomial P (\*) n (x). We prove that the function [\*+(2n 2 +1)Γ (4n+2)] 1Γ2 x (\*) n, k increases as \* increases for \*> &1Γ2. The proof is based on two integrals involved with the s