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On the coefficients of differentiated expansions of ultraspherical polynomials

โœ Scribed by Andreas Karageorghis; Timothy N. Phillips


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
911 KB
Volume
9
Category
Article
ISSN
0168-9274

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## Let x (*) n, k , k=1, 2, ..., [nร‚2], denote the k th positive zero in increasing order of the ultraspherical polynomial P (\*) n (x). We prove that the function [\*+(2n 2 +1)ร‚ (4n+2)] 1ร‚2 x (\*) n, k increases as \* increases for \*> &1ร‚2. The proof is based on two integrals involved with the s