Gram Polynomials and the Kummer Function

✍ Scribed by R.W Barnard; G Dahlquist; K Pearce; L Reichel; K.C Richards

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 279 KB
• Volume: 94
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1998.3181

✦ Synopsis

Let [, k ] n k=0 , n<m, be a family of polynomials orthogonal with respect to the positive semi-definite bilinear form

x j :=&1+(2j&1)Âm. These polynomials are known as Gram polynomials. The present paper investigates the growth of |, k (x)| as a function of k and m for fixed x # [&1, 1]. We show that when n 2.5m 1Â2 , the polynomials in the family [, k ] n k=0 are of modest size on [&1, 1], and they are therefore well suited for the approximation of functions on Article No. AT983181 128