Local asymptotics of the~ratio of orthogonal polynomials in the~neighbourhood of an~end-point of the~support of the~orthogonality measure
Sbornik. Mathematics, Tome 192 (2001) no. 2, pp. 299-321
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A new method of studying the asymptotic behaviour of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure is put forward. The asymptotics in the neighbourhood of the end-point is found in terms of the asymptotics of the values of the polynomials at the point itself and the asymptotic behaviour of the coefficients of the recurrence relations. Applications of the result obtained are considered.
@article{SM_2001_192_2_a7,
author = {D. N. Tulyakov},
title = {Local asymptotics of the~ratio of orthogonal polynomials in the~neighbourhood of an~end-point of the~support of the~orthogonality measure},
journal = {Sbornik. Mathematics},
pages = {299--321},
publisher = {mathdoc},
volume = {192},
number = {2},
year = {2001},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2001_192_2_a7/}
}
TY - JOUR AU - D. N. Tulyakov TI - Local asymptotics of the~ratio of orthogonal polynomials in the~neighbourhood of an~end-point of the~support of the~orthogonality measure JO - Sbornik. Mathematics PY - 2001 SP - 299 EP - 321 VL - 192 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2001_192_2_a7/ LA - en ID - SM_2001_192_2_a7 ER -
%0 Journal Article %A D. N. Tulyakov %T Local asymptotics of the~ratio of orthogonal polynomials in the~neighbourhood of an~end-point of the~support of the~orthogonality measure %J Sbornik. Mathematics %D 2001 %P 299-321 %V 192 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2001_192_2_a7/ %G en %F SM_2001_192_2_a7
D. N. Tulyakov. Local asymptotics of the~ratio of orthogonal polynomials in the~neighbourhood of an~end-point of the~support of the~orthogonality measure. Sbornik. Mathematics, Tome 192 (2001) no. 2, pp. 299-321. http://geodesic.mathdoc.fr/item/SM_2001_192_2_a7/