The Steepest-Descent Method - ppt download

Steepest-Descent Method Complex Integral: The method was published by Peter Debye in Debye noted in his work that the method was developed in a unpublished note by Bernhard Riemann (1863). Peter Joseph William Debye (March 24, 1884 – November 2, 1966) was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry. Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity.
Hence we have: as. Note: In a similar manner, we could obtain higher-order terms in the asymptotic expansion of the Bessel function or the Gamma function.

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The Steepest-Descent Method - ppt download