Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 336 / 1 / c / i

Table of contents
- Solution i

Solution

For

F (t) = sech α sinh t - t

, the relevant saddle point is

t = α

, where

F (α) = tanh α - α

and

F^{''} (α) = tanh α

. The method of steepest descent gives

J_{ν} (ν sech α) \sim \frac{exp [ ν ( tanh α - α )]}{2 π ν tanh α} (α > 0) .

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version