TY - JOUR
T1 - Szegö‘s conjecture on lebesgue constants for Legendre series
AU - Qu, C. K.
AU - Wong, R.
PY - 1988/11
Y1 - 1988/11
N2 - In 1926, Szegö conjectured that the Lebesgue constants for Legendre series form a monotonically increasing sequence. In this paper, we prove that his conjecture is true. Our method is based on an asymptotic expansion together with an explicit error bound, and makes use of some recent results of Baratella and Gatteschi concerning uniform asymptotic approximations of the Jacobi polynomials. © 1988 by Pacific Journal of Mathematics.
AB - In 1926, Szegö conjectured that the Lebesgue constants for Legendre series form a monotonically increasing sequence. In this paper, we prove that his conjecture is true. Our method is based on an asymptotic expansion together with an explicit error bound, and makes use of some recent results of Baratella and Gatteschi concerning uniform asymptotic approximations of the Jacobi polynomials. © 1988 by Pacific Journal of Mathematics.
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U2 - 10.2140/pjm.1988.135.157
DO - 10.2140/pjm.1988.135.157
M3 - RGC 21 - Publication in refereed journal
SN - 0030-8730
VL - 135
SP - 157
EP - 188
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 1
ER -