saddle-point method

saddle-point method

[′sad·əl ¦pȯint ‚meth·əd]
(mathematics)
steepest-descent method
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Keywords: analytic functions, Airy phenomena, asymptotics, coalescing saddle-point method, multivariable generating functions, polynomial canonical representations
In particular, the asymptotic analysis of the above integral is amenable for the saddle-point method to obtain uniform asymptotic expansions for the coefficients in (4) for ([n.sub.0], n) [member of ] [parallel]([n.sub.0], n) JI .
In order to apply the saddle-point method let 1 be the order of vanishing of F about (0; ([t.sub.0], t); x([t.sub.0], t)) with respect to the variable [theta].