RT Journal Article
T1 On modified asymptotic series involving confluent hypergeometric functions
A1 Deaño Cabrera, Alfredo
A1 Temme, Nico M.
AB A modification of standard Poincaré asymptotic expansions for functions defined by means of Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptoticexpansion involves confluent hypergeometric functions U(a,c,z), which can be computed by means of continued fractions in a backward recursion scheme. Numerical examples are included, such as the incomplete gamma function Γ(a,z) and the modified Bessel function Kv(z) for large values of z. It is observed that the same procedure can be applied to uniform asymptotic expansions when extra parameters become large as well.
PB Kent State University
SN 1068-9613
YR 2009
FD 2009
LK https://hdl.handle.net/10016/6637
UL https://hdl.handle.net/10016/6637
LA eng
NO 16 pages, 5 figures.-- MSC2000 codes: 33C15, 33F99, 34E05, 30E15, 40A05.
NO The first author acknowledges financial support from the Program of postdoctoral research grants (Programa de becas postdoctorales) of the Spanish Ministry of Education and Science (Ministerio de Educación y Ciencia). The authors acknowledge financial support from the Spanish Ministry of Education and Science (Ministerio de Educación yCiencia), under project MTM2006–09050.
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RD 2 may. 2024