T. Mark Dunster
Professor
Department of Mathematics and Statistics
College of Sciences
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-7720
U.S.A.
email:
mdunster<AT>mail<DOT>sdsu<DOT>edu
Tel. (619) 594 5968
Fax. (619) 594 2029
Office: GMCS-521
Research Areas:
Asymptotic analysis, special functions, ordinary differential equations.
Publications
in Refereed Journals
[1] 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.
[2] T. M.
Dunster, Uniform asymptotic expansions
for prolate spheroidal functions with large parameters. SIAM J. Math. Anal., 17 (6) (1986) pp. 1495-1524.
[3] T. M.
Dunster, Uniform asymptotic
expansions for Whittaker's confluent hypergeometric functions. SIAM J. Math. Anal., 20 (3) (1989) pp. 744-760.
[4] 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.
[5] 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.
[6] T. M.
Dunster and D. A. Lutz, Convergent
factorial series expansions for Bessel functions. SIAM J. Math. Anal., 22 (4) (1991) pp. 1156-1172.
[7] T. M.
Dunster, Conical functions with
one or both parameters large. Proc.
Roy. Soc. Edinburgh Sec. A, 119A (1991) pp. 311-327.
[8] T. M.
Dunster, Uniform asymptotic
expansions for oblate spheroidal functions I: positive separation parameter l. Proc. Roy. Soc.
Edinburgh Sec. A, 122A (1992) pp. 303-320.
[9] 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.
[10] T. M. Dunster, Uniform asymptotic approximations for Mathieu
functions. Methods and Applications
of Analysis,1 (2) (1994) pp. 143-168.
[11] 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.
[12] T. M. Dunster, Uniform asymptotic expansions for oblate spheroidal
functions II: negative separation parameter l.
Proc. Roy. Soc. Edinburgh Sec. A, 125A (1995) pp. 719-737.
[13] 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.
[14] 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.
[15] T. M. Dunster, Error bounds for exponentially improved
asymptotic solutions of ordinary differential equations having irregular
singularities of rank one. Methods and
Applications of Analysis, 3 (1) (1996) pp. 109-134.
[16] T. M. Dunster, Error analysis in a uniform asymptotic expansion
for the generalised exponential integral.
J. Comp. and App. Math., 80 (1997) pp. 127-161.
[17] 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.
[18] T. M. Dunster, Asymptotics of the eigenvalues of a rotating
harmonic oscillator. J. Comp. and App. Math. 93 (1998) pp.
45-73.
[19] T. M. Dunster, Uniform asymptotic approximations for the Jacobi
and ultraspherical polynomials, and related functions. Methods and Applications of Analysis, 6 (3) (1999)
pp. 281-316.
[20] 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.
[21] T. M. Dunster, Convergent expansions for linear ordinary differential
equations having a simple turning point, with an application to Bessel
functions. Studies in Applied Math.,
107 (2001) pp. 293-323.
[22] T. M. Dunster, Uniform asymptotic expansions for Charlier
polynomials. J. Approx. Theory, 112
(2001) pp. 93-133.
[23] T. M. Dunster, Uniform asymptotic expansions for associated
Legendre functions of large order.
Proc. Roy. Soc. Edinburgh Sec. A, 133A, (2003) pp. 807-827.
[24] T. M. Dunster, Uniform asymptotic approximations for the
Whittaker functions W and M. Analysis
and Applications, 1 (2003) pp. 199-212.
[25] T. M. Dunster, Convergent expansions for solutions of linear
ordinary differential equations having a simple pole, with an application to
associated Legendre functions,
Studies in Applied Math., 113 (2004) pp. 245-270.
[26] T. M. Dunster, Uniform asymptotic approximations for incomplete
Riemann zeta functions, J. Comput.
Appl. Math. 190 (2006), pp. 339-353.
[27] T. M. Dunster, M. Yedlin, K.
Lam, Resonance and the late
coefficients in the scattered field of a dielectric circular cylinder, Anal. Appl. 4 (2006), pp. 311-333.
[28] T. M. Dunster, On the logarithmic derivative of Nicholson’s
integral, Anal. Appl. 7 (2009), pp.
73-86.
[29] T. M. Dunster, Quasi Nonuniqueness in the Scattered Field of a
Dielectric Circular Cylinder, Anal.
Appl. 8 (2010), pp. 63-83.
[30] T. M. Dunster, Simplified asymptotic solutions of differential
equations having double turning points, with an application to the incomplete
gamma function, Studies in Applied
Math. (2011), http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9590.2011.00519.x/pdf.
[31] T. M. Dunster, Conical functions of purely imaginary order and
argument. (2011, submitted to Proc.
Roy. Soc. Edinburgh Sec. A). http://www-rohan.sdsu.edu/~dunster/Conicalfunctions.pdf
Legendre and related functions. NIST handbook of mathematical functions, 351–381,
U.S. Dept. Commerce, Washington, DC, 2010, http://dlmf.nist.gov/14