TY - GEN
T1 - Uniform Asymptotic Expansions
AU - WONG, Sue Cheun Roderick
PY - 2001
Y1 - 2001
N2 - In this lecture, I first review an extension of the method of steepest descents given by (1957). This extension allows one to derive asymptotic expansions which hold uniformly in regions where two saddle points may coalesce at a single point. As an illustration, I give an outline of a derivation of a uniform asymptotic expansion of the Hermite polynomial Hn(√2n+1t) . Next, I present a modification of the method of Chester, Friedman and Ursell, which can handle situations where two saddle points may coalesce at two distinct locations. Such situations occur in the cases of Meixner, Meixner-Pollaczek, and Krawtchouk polynomials. © Kluwer Academic Publishers 2001
AB - In this lecture, I first review an extension of the method of steepest descents given by (1957). This extension allows one to derive asymptotic expansions which hold uniformly in regions where two saddle points may coalesce at a single point. As an illustration, I give an outline of a derivation of a uniform asymptotic expansion of the Hermite polynomial Hn(√2n+1t) . Next, I present a modification of the method of Chester, Friedman and Ursell, which can handle situations where two saddle points may coalesce at two distinct locations. Such situations occur in the cases of Meixner, Meixner-Pollaczek, and Krawtchouk polynomials. © Kluwer Academic Publishers 2001
U2 - 10.1007/978-94-010-0818-1_18
DO - 10.1007/978-94-010-0818-1_18
M3 - RGC 32 - Refereed conference paper (with host publication)
SN - 978-0-7923-7120-5
T3 - NATO Science Series II: Mathematics, Physics and Chemistry
SP - 489
EP - 503
BT - Special Functions 2000: Current Perspective and Future Directions
A2 - Bustoz, Joaquin
A2 - Ismail, Mourad E. H.
A2 - Suslov, Sergei K.
PB - Springer
CY - Dordrecht
ER -