TY - JOUR
T1 - Uniform asymptotic expansions of the Tricomi-Carlitz polynomials
AU - LEE, Kei Fung
AU - Wong, R.
PY - 2010/7
Y1 - 2010/7
N2 - The Tricomi-Carlitz polynomials satisfy the second-order linear difference equation (n + 1)fn+1
(α) (x) - (n + α)x f n
(α) (x) + fn-1
(α) (x) = 0, n≥ 1, with initial values f0
(α) (x) = 1 and f1
(α) (x) = αx, where x is a real variable and α is a positive parameter. An asymptotic expansion is derived for these polynomials by using the turning-point theory for three-term recurrence relations developed by Wang and Wong [Numer. Math. 91(2002) and 94(2003)]. The result holds uniformly in regions containing the critical values x = ±2/√v , here ? = n + 2α - 1/2. © 2010 American Mathematical Society.
AB - The Tricomi-Carlitz polynomials satisfy the second-order linear difference equation (n + 1)fn+1
(α) (x) - (n + α)x f n
(α) (x) + fn-1
(α) (x) = 0, n≥ 1, with initial values f0
(α) (x) = 1 and f1
(α) (x) = αx, where x is a real variable and α is a positive parameter. An asymptotic expansion is derived for these polynomials by using the turning-point theory for three-term recurrence relations developed by Wang and Wong [Numer. Math. 91(2002) and 94(2003)]. The result holds uniformly in regions containing the critical values x = ±2/√v , here ? = n + 2α - 1/2. © 2010 American Mathematical Society.
KW - Difference equation
KW - Tricomi-Carlitz polynomials
KW - Uniform asymptotic expansion
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U2 - 10.1090/S0002-9939-10-10301-3
DO - 10.1090/S0002-9939-10-10301-3
M3 - RGC 21 - Publication in refereed journal
SN - 0002-9939
VL - 138
SP - 2513
EP - 2519
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -