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 ë.
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
Mκ,iμ(z)
and Wκ,iμ(z)
. Anal. Appl. 1 (2) (2003), 199-212.
- T. M. Dunster, Convergent expansions for
solutions of linear ordinary differential equations having a
simple pole, with an application to associated Legendre
functions. Stud. Appl. Math. 113 (3) (2004), 245-270.
- T. M. Dunster, Uniform asymptotic
approximations for incomplete Riemann zeta functions. J. Comput. Appl. Math. 190 (1-2) (2006),
339-353.
- T. M. Dunster, M. Yedlin and K. Lam,
Resonance and the late coefficients in the scattered field of
a dielectric circular cylinder. Anal. Appl. 4 (4) (2006),
311-333.
- T. M. Dunster,
On the logarithmic derivative of Nicholson’s integral. Anal.
Appl. 7 (1) (2009), 73-86.
- T. M. Dunster, Quasi nonuniqueness
in the scattered field of a dielectric circular cylinder.
Anal. Appl. 8 (1) (2010), 63-83.
- T. M. Dunster, Simplified
asymptotic solutions of differential equations having double
turning points, with an application to Legendre functions.
Stud. Appl. Math. 127 (3) (2011), 250-283.
- T. M. Dunster, Conical functions of purely
imaginary order and argument. Proc. Roy. Soc. Edinburgh Sec.
A. 143 (5) (2013), 929-955.
- T. M. Dunster, Electromagnetic wave
scattering by two parallel infinite dielectric cylinders.
Stud. Appl. Math. 131 (3) (2013), 302-316.
- T. M. Dunster, Olver’s
error bound methods applied to linear ordinary differential
equations having a simple turning point. Anal. Appl. 12 (4)
(2014), 385-402.
- T. M. Dunster, A. Gil, J. Segura and N. M. Temme, Computation of a numerically
satisfactory pair of solutions of the differential equation
for conical functions of non-negative integer orders. Numer. Algorithms 68 (2015), 497-509.
- T. M. Dunster, On the order derivatives of
Bessel functions. Constr. Approx. 46 (1) (2017), 47-68.
-
T. M. Dunster, Asymptotics of prolate spheroidal wave
functions. J. Classical Anal. 11 (1) (2017), 1-21.
- T. M. Dunster, A. Gil and J. Segura, Computation of asymptotic
expansions of turning point problems via Cauchy's integral
formula: Bessel functions. Constr. Approx. 46 (3) (2017),
645-675.
- T. M. Dunster, A. Gil, J. Segura and N. M.
Temme, Conical: an extended
module for computing a numerically satisfactory pair of
solutions of the differential equation for conical
functions. Comput. Phys. Commun. 217 (2017), 193-197.
- T. M. Dunster, A. Gil and J. Segura,
Uniform asymptotic expansions for Laguerre polynomials and
related confluent hypergeometric functions. Adv. Comput. Math. 44 (5) (2018),
1441-1474.
- H. S. Cohl, T. H. Dang and T. M. Dunster, Fundamental solutions and Gegenbauer expansions of Helmholtz
operators on Riemannian spaces of constant curvature. SIGMA
14 (2018), 136, 45 pages. https://www.emis.de/journals/SIGMA/2018/136/sigma18-136.pdf
- T. M. Dunster, Liouville-Green expansions
of exponential form, with an application to modified Bessel
functions. Proc. Roy. Soc. Edinburgh Sec. A. 150
(3) (2020), 1289-1311.
- T. M. Dunster,
Asymptotic solutions of inhomogeneous differential
equations having a turning point. Stud. Appl. Math.
145 (3) (2020), 500-536.
- T. M. Dunster, A. Gil and J. Segura,
Simplified error bounds for turning point expansions. Anal.
Appl. 19 (4) (2021), 647-678.
- T. M. Dunster,
Uniform
asymptotic
expansions for
solutions of the
parabolic cylinder
and Weber equations.
J.
Classical Anal.
17 (1)
(2021),
69-107.
- T. M. Dunster,
A. Gil and J.
Segura, Sharp
error bounds
for turning
point
expansions. J.
Classical
Anal.
18 (1) (2021),
49-81.
- T. M. Dunster,
Nield-Kuznetsov
functions and
Laplace
transforms of
parabolic
cylinder
functions. SIAM J.
Math. Anal. 53
(5), (2021)
5915-5947.
- T. M. Dunster,
Uniform
asymptotic
expansions for
the Whittaker
functions M
κ,μ(z) and Wκ,μ(z) with μ
large. Proc.
A. 477 (2021),
no. 2252,
Paper No.
20210360, 18
pp., https://doi.org/10.1098/rspa.2021.0360
- T. M.