کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4606937 | 1631412 | 2015 | 48 صفحه PDF | دانلود رایگان |
E. Heine in the 19th century studied a system of orthogonal polynomials associated with the weight [x(x−α)(x−β)]−12, x∈[0,α]x∈[0,α], 0<α<β0<α<β. A related system was studied by C. J. Rees in 1945, associated with the weight [(1−x2)(1−k2x2)]−12, x∈[−1,1]x∈[−1,1], k2∈(0,1)k2∈(0,1). These are also known as elliptic orthogonal polynomials, since the moments of the weights may be expressed in terms of elliptic integrals. Such orthogonal polynomials are of great interest because the corresponding Hankel determinant, depending on a parameter k2k2, where 0
Journal: Journal of Approximation Theory - Volume 198, October 2015, Pages 63–110