Explicit Series Formulae for the Evaluation of Integrals by the Method of Steepest Descents | Zendy

Campbell John A. | Zendy; Fröman Per Olof | Zendy; Walles Erik | Zendy

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Explicit Series Formulae for the Evaluation of Integrals by the Method of Steepest Descents

Author(s) -

Campbell John A.,

Fröman Per Olof,

Walles Erik

Publication year - 1987

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm1987772151

Subject(s) - saddle point , mathematics , series (stratigraphy) , saddle , zero (linguistics) , order (exchange) , point (geometry) , explicit formulae , mathematical analysis , pure mathematics , mathematical optimization , geometry , paleontology , linguistics , philosophy , finance , economics , biology

Explicit series formulae are given for use in the method of steepest descents, where it is required to find the contribution to an integral of the form ∫e vw ( z ) φ ( z ) dz from a well‐isolated saddle point z 0 . Here v is a large positive parameter, and w ( N ) ( z 0) ≠ 0 while lower‐order derivatives at z 0 are equal to zero. Examples where the formulae are helpful are presented.

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