# Discrete Laplace Method and Truncation Error of Gauss Continued Fraction

## TL;DR

This paper precisely determines the asymptotic truncation error of Gauss's continued fraction and generalizes the discrete Laplace method for hypergeometric series with large parameters, enhancing analytical tools in special functions.

## Contribution

It provides an exact asymptotic analysis of the truncation error and extends the discrete Laplace method for broader application to hypergeometric series.

## Key findings

- Exact asymptotics of Gauss's continued fraction truncation error
- Generalized discrete Laplace method for hypergeometric series
- Broader applicability of asymptotic analysis techniques

## Abstract

The leading asymptotics of the truncation error for Gauss's continued fraction is determined exactly. Not only for this purpose but also for wider applicability elsewhere the discrete analogue of Laplace's method for hypergeometric series containing a large parameter, which was developed in a previous paper, is generalized in two directions.