T. Mark
Dunster
Ph.D. Applied
Mathematics,
University of Bristol, U.K.
Professor, Department of Mathematics & Statistics
College of Sciences
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-7720
USA
Research Areas: Asymptotic analysis, special functions,
ordinary differential equations, scattering theory.
Publications
- W. G .C. Boyd and T. M.
Dunster, Uniform asymptotic solutions of a class of second-order
linear differential equations having a turning point and a
regular singularity, with an application to Legendre functions.
SIAM J. Math. Anal. 17 (2) (1986), 422-450.
- T. M. Dunster, Uniform asymptotic expansions for prolate
spheroidal functions with large parameters. SIAM J. Math. Anal.
17 (6) (1986), 1495-1524.
- T. M. Dunster, Uniform asymptotic expansions for Whittaker's
confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3)
(1989), 744-760.
- T. M. Dunster, Bessel
functions of purely imaginary order, with an application to
second-order linear differential equations having a large
parameter. SIAM J. Math. Anal. 21 (4) (1990), 995-1018.
- T. M. Dunster, Uniform asymptotic solutions of second-order
linear differential equations having a double pole with complex
exponent and a coalescing turning point. SIAM J. Math. Anal. 21
(6) (1990), 1594-1618.
- T. M. Dunster and D. A. Lutz, Convergent factorial series
expansions for Bessel functions. SIAM J. Math. Anal. 22 (4)
(1991), 1156-1172.
- T. M. Dunster, Conical
functions with one or both parameters large. Proc. Roy. Soc.
Edinburgh Sec. A 119 (3-4) (1991), 311-327.
- T. M. Dunster, Uniform asymptotic expansions for oblate
spheroidal functions I: positive separation parameter λ.
Proc. Roy. Soc. Edinburgh Sec. A 121 (3-4) (1992), 303-320.
- T. M. Dunster, D. A. Lutz and R. Schäfke, Convergent
Liouville-Green expansions for second-order linear differential
equations, with an application to Bessel functions. Proc. Roy.
Soc. London, Ser. A 440 (1993), 37-54.
- T. M. Dunster, Uniform asymptotic approximations for Mathieu
functions. Methods Appl. Anal. 1 (2) (1994), 143-168.
- T. M. Dunster, Uniform asymptotic solutions of second-order
linear differential equations having a simple pole and a
coalescing turning point in the complex plane. SIAM J. Math.
Anal. 25 (2)
(1994), 322-353.
- T. M. Dunster, Uniform asymptotic expansions for oblate
spheroidal functions II: negative separation parameter λ. Proc. Roy. Soc.
Edinburgh Sec. A 125 (4) (1995), 719-737.
- T. M. Dunster, Asymptotics of the generalised exponential
integral, and error bounds in the uniform asymptotic smoothing
of its Stokes' discontinuities. Proc. Roy. Soc. London Ser. A 452 (1996), 1351-1367.
- T. M. Dunster, Asymptotic solutions of second-order linear
differential equations having almost coalescent turning points,
with an application to the incomplete Gamma function. Proc. Roy.
Soc. London Ser. A 452
(1996), 1331-1349.
- T. M. Dunster, Error bounds for exponentially improved
asymptotic solutions of ordinary differential equations having
irregular singularities of rank one. Methods Appl. Anal. 3 (1)
(1996), 109-134.
- T. M. Dunster, Error
analysis in a uniform asymptotic expansion for the generalised
exponential integral. J. Comp. Appl. Math. 80 (1) (1997),
127-161.
- T. M. Dunster, R. B. Paris and S. Cang, On the high-order
coefficients in the uniform asymptotic expansion for the
incomplete Gamma function. Methods Appl. Anal. 5 (3) (1998),
223-247.
- T. M. Dunster, Asymptotics of the eigenvalues of a rotating
harmonic oscillator. J.
Comp. Appl. Math. 93 (1) (1998), 45-73.
- T. M. Dunster, Uniform asymptotic approximations for the
Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3) (1999), 281-316.
- T. M. Dunster, Uniform
asymptotic expansions for the reverse generalised Bessel
polynomials, and related functions. SIAM J. Math. Anal. 32 (5)
(2001), 987-1013.
- T. M. Dunster, Convergent expansions for linear ordinary
differential equations having a simple turning point, with an
application to Bessel functions. Stud. Appl. Math. 107 (3)
(2001), 293-323.
- T. M. Dunster, Uniform asymptotic expansions for Charlier
polynomials. J. Approx. Theory 112 (1) (2001), 93-133.
- T. M. Dunster, Uniform
asymptotic expansions for associated Legendre functions of large
order. Proc. Roy. Soc. Edinburgh Sec. A, 133 (4) (2003),
807-827.
- T. M. Dunster, Uniform
asymptotic approximations for the Whittaker functions