David Kaminski
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Degrees
B.Sc. (Hons.), M.A., Ph.D. (Mathematics)Expertise
Asymptotics and special functions, Asymptotics of functions defined by Laplace-type integrals and Mellin-Barnes integrals, Hadamard expansions of solutions of differential equations and integral representationsResearch Areas
Hadamard expansions of singular perturbation problems, Hadamard expansions of certain Painlevé I solutions, Hadamard convolutions, Elliptic asymptotics of the Painlevé I transcendentPrevious Research Areas
Asymptotics and special functions, Asymptotics of functions defined by Laplace-type integrals and Mellin-Barnes integrals, Hadamard expansions of solutions of differential equations and integral representations, Multidimensional steepest descents, Uniform asymptotics of diffraction integralsSelected Publications
Kaminski, D. and R. B. Paris. Asymptotics & Mellin-Barnes Integrals. Cambridge, England: Cambridge University Press, 2000.Kaminski, D. and R. B. Paris. Asymptotics of a class of multidimensional Laplace-type integrals. I. Double integrals. Phil. Trans. R. Soc. Lond. 356 (1998): 583-623.
Kaminski, D. and R. B. Paris. Asymptotics of a class of multidimensional Laplace-type integrals. I. Treble integrals. Phil. Trans. R. Soc. Lond. 356 (1998): 625-667.
Kaminski, D. and R. B. Paris. On the zeroes of the Pearcey integral. J. Computational and Appl. Math. 107 (1999) 31-52.
Kaminski, D. and R. B. Paris. On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type. Proc. R. Soc. Edin. 134A (2004): 159-178.
Paris, R. B. and D. Kaminski. Hadamard expansions for integrals with saddles coalescing with an endpoint. Applied Math. Letters 18(2005): 1389-1395
Paris, R. B. and D. Kaminski. Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions. J. Computational and Appl. Math. 190(2006): 437-452
Research Interests
David Kaminski has been with the Department of Mathematics and Computer Science for over a decade. His active research interests are in the area of asymptotics and special functions, with particular focus on the asymptotics of functions defined by Laplace-type integrals and Mellin-Barnes integrals. Recently, his investigations have widened to include nonlinear difference equations associated with orthogonal polynomials with Freud weights. These problems arise in the mathematics frequently found in applications from physical science and engineering. His work in these areas is NSERC funded.Current Research and Creative Activity
| Title | Location | Grant Information | Principal Investigator | Co Researchers |
|---|---|---|---|---|
| Elliptic asymptotics of the Painlevé I transcendent | Lethbridge, AB | David Kaminski, University of Lethbridge | Richard Paris, University of Abertay Dundee |
Previous Research
| Title | Grant Agency | Completion Date |
|---|---|---|
| Hyperasymptotic expansions of solutions to differential equations | Natural Sciences and Engineering Research Council (NSERC) | 2003 |
| Quadratic difference equations | Natural Sciences and Engineering Research Council (NSERC) | 2004 |
| Hyperasymptotic evaluation of integrals of Laplace type | NA | 2005 |