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 
  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 119 (3-4) (1991), pp. 311-327.
  8. 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.
  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 Appl. Anal.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 λ. Proc. Roy. Soc. Edinburgh Sec. A 125 (4) (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 Appl. Anal. 3 (1) (1996), pp. 109-134.
  16. T. M. Dunster, Error analysis in a uniform asymptotic expansion for the generalised exponential integral. J. Comp. Appl. 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. Appl. Math. 93 (1) (1998), pp. 45-73.
  19. T. M. Dunster, Uniform asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions. Methods Appl. Anal. 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. Stud. Appl. Math. 107 (3) (2001), pp. 293-323.
  22. T. M. Dunster, Uniform asymptotic expansions for Charlier polynomials. J. Approx. Theory 112 (1) (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 Mκ,iμ and Wκ,iμ. Anal. Appl. 1 (2) (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. Stud. Appl. Math. 113 (3) (2004), pp. 245-270.
  26. T. M. Dunster, Uniform asymptotic approximations for incomplete Riemann zeta functions. J. Comput. Appl. Math. 190 (1-2) (2006), pp. 339-353.
  27. 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.
  28. T. M. Dunster, On the logarithmic derivative of Nicholson’s integral. Anal. Appl. 7 (1) (2009), pp. 73-86.
  29. T. M. Dunster, Quasi nonuniqueness in the scattered field of a dielectric circular cylinder. Anal. Appl. 8 (1) (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. Stud. Appl. Math. 127 (3) (2011),  pp. 250-283.
  31. T. M. Dunster, Conical functions of purely imaginary order and argument. Proc. Roy. Soc. Edinburgh Sec. A 143 (2013), pp. 929-955.
  32. T. M. Dunster, Electromagnetic wave scattering by two parallel infinite dielectric cylinders. Stud. Appl. Math. 131 (2013), pp. 302-316.
  33. T. M. Dunster, Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. 12 (2014), pp. 385-402.
  34. 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), http://dx.doi.org/10.1007/s11075-014-9857-5.
Book Chapter

             Legendre and related functions. NIST handbook of mathematical functions, 351–381, U.S. Dept. Commerce, Washington, DC, 2010, http://dlmf.nist.gov/14