Professor, Department of Mathematics & Statistics

College of Sciences

San Diego State University

5500 Campanile Drive

San Diego, CA 92182-7720

USA

- 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), pp. 422-450.
- T. M. Dunster, Uniform asymptotic expansions for prolate
spheroidal functions with large parameters. SIAM J. Math. Anal.
17 (6) (1986), pp. 1495-1524.
- T. M. Dunster, Uniform asymptotic expansions for Whittaker's
confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3)
(1989), pp. 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), pp. 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), pp. 1594-1618.
- T. M. Dunster and D. A. Lutz, Convergent factorial series
expansions for Bessel functions. SIAM J. Math. Anal. 22 (4)
(1991), pp. 1156-1172.
- T. M. Dunster, Conical
functions with one or both parameters large. Proc. Roy. Soc.
Edinburgh Sec. A 119 (3-4) (1991), pp. 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), pp. 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), pp. 37-54.
- T. M. Dunster, Uniform asymptotic approximations for Mathieu
functions. Methods Appl. Anal.1 (2) (1994), pp. 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), pp. 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), pp. 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), pp.
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), pp. 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), pp. 109-134.
- T. M. Dunster, Error
analysis in a uniform asymptotic expansion for the generalised
exponential integral. J. Comp. Appl. Math. 80 (1997), pp.
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), pp.
223-247.
- T. M. Dunster, Asymptotics of the eigenvalues of a rotating
harmonic oscillator. J.
Comp. Appl. Math. 93 (1) (1998), pp. 45-73.
- T. M. Dunster, Uniform asymptotic approximations for the
Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3) (1999), pp. 281-316.
- T. M. Dunster, Uniform
asymptotic expansions for the reverse generalised Bessel
polynomials, and related functions. SIAM J. Math. Anal. 32 (5)
(2001), pp. 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), pp. 293-323.
- T. M. Dunster, Uniform asymptotic expansions for Charlier
polynomials. J. Approx. Theory 112 (1) (2001), pp. 93-133.
- T. M. Dunster, Uniform
asymptotic expansions for associated Legendre functions of large
order. Proc. Roy. Soc. Edinburgh Sec. A 133A (2003), pp.
807-827.
- T. M. Dunster, Uniform
asymptotic approximations for the Whittaker functions
*M*_{κ,iμ}_{}and*W*_{κ,iμ}. Anal. Appl. 1 (2) (2003), pp. 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), pp. 245-270.
- T. M. Dunster, Uniform asymptotic approximations for
incomplete Riemann zeta functions. J. Comput. Appl. Math. 190
(1-2) (2006), pp. 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) pp. 311-333.
- T. M. Dunster, On the
logarithmic derivative of Nicholson’s integral. Anal. Appl. 7
(1) (2009), pp. 73-86.
- T. M. Dunster, Quasi nonuniqueness in the scattered field of a
dielectric circular cylinder. Anal. Appl. 8 (1) (2010), pp.
63-83.
- T. M. Dunster, Simplified asymptotic solutions of differential
equations having double turning points, with an application to
the incomplete gamma function. Stud. Appl. Math. 127 (3) (2011), pp. 250-283.
- T. M. Dunster, Conical functions of purely imaginary order and
argument. Proc. Roy. Soc. Edinburgh Sec. A 143 (2013), pp.
929-955.
- T. M. Dunster, Electromagnetic wave scattering by two parallel
infinite dielectric cylinders. Stud. Appl. Math. 131 (2013), pp.
302-316.
- T. M. Dunster, Olver’s error bound methods applied to linear
ordinary differential equations having a simple turning point.
Anal. Appl (2014), to appear.
- 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 (2014), submitted.