Asymptotics of the generalized exponential integral, and. error bounds in the uniform asymptotic smoothing of its Stokes discontinuities

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1949, 1996, Pages 1351-1367

  Dunster, T A I ^a  

^a SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23744501580     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0069     Document Type: Article

References (9)

1. Berry, M. V. 1989 Uniform asymptotic smoothing of Stokes's discontinuities. Proc. R. Soc. Land. A 422, 7-21.
2. Dunster, T. M. 1996 Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function. Proc. R. Soc. Land. A 452, 1331-1349. (Preceding paper.)
3. Jones, D. S. 1990 In Uniform asymptotic remainders in asymptotic and computational analysis (ed. R. Wong), pp. 241-264. New York: Marcel Dekker.
4. McLeod, J. B. 1992 Smoothing of Stokes's discontinuities. Proc. R. Soc. Land. A 437, 343-354.
5. Olde Daalhuis, A. B. & Olver, F. \V. J. 1994 Exponentially improved asymptotic solutions of ordinary differential equations. II. Irregular singularities of rank one. Proc. R. Soc. Land. A 445, 39-56.
6. Olver, F. W. J. 1974 Asymptotics and special functions. New York: Academic Press.
7. Olver, F. W. J. 1991 Uniform, exponentially improved asymptotic expansions for the generalized exponential integral. SIAM J. Math. Analysis 22, 1460-1489.
8. Paris, R. B. 1992 Smoothing of the Stokes phenomenon for high order differential equations. Proc. R. Soc. Land. A 436, 165-186.
9. Temme, N. M. 1979 The asymptotic expansion of the incomplete gamma functions. SIAM J. Math. Analysis 10, 757-766.