Geodesic
A simplification of the Laplace method for double integrals. Application to the second Appell function
Electronic transactions on numerical analysis, Tome 30 (2008), pp. 224-236
The main difficulties in the Laplace method of asymptotic expansions of double integrals result from a change of variables. Generalizing previous work for simple integrals, we propose a variant of the method for double integrals, which avoids this change of variables and simplifies the computations. The calculation of the coefficients of the asymptotic expansion is remarkably simple. Moreover, the asymptotic sequence is as simple as in the standard Laplace's method: inverse powers of the asymptotic variable. A new asymptotic expansion of the second Appell's function for large , , and is given as an illustration.
Classification : 41A60, 41A58, 33C65
Keywords: asymptotic expansions of integrals, Laplace method for double integrals, second Appell function 
@article{ETNA_2008__30__a12,
     author = {L\'opez,  Jos\'e L. and Pagola,  Pedro J.},
     title = {A simplification of the {Laplace} method for double integrals. {Application} to the second {Appell} function},
     journal = {Electronic transactions on numerical analysis},
     pages = {224--236},
     year = {2008},
     volume = {30},
     zbl = {1176.41036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__30__a12/}
}
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López,  José L.; Pagola,  Pedro J. A simplification of the Laplace method for double integrals. Application to the second Appell function. Electronic transactions on numerical analysis, Tome 30 (2008), pp. 224-236. http://geodesic.mathdoc.fr/item/ETNA_2008__30__a12/