Abstract
The method of steepest descents or saddle-point method is essentially a generalization of Laplace’s method to integrals in the complex plane. The method originated with Riemann†. It was developed in its present form independently by Debye ‡. Various extensions and rigorous proofs of some of the procedures have been given since their work and some of these are in the books cited. The basic idea and method which still has the widest applicability, are discussed in this section, with several illustrative worked examples being given in §3.2.
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© 1984 Springer Science+Business Media New York
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Murray, J.D. (1984). Method of steepest descents. In: Asymptotic Analysis. Applied Mathematical Sciences, vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1122-8_3
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DOI: https://doi.org/10.1007/978-1-4612-1122-8_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7015-7
Online ISBN: 978-1-4612-1122-8
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