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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2009 • Question 10

Question

Math 6420 • PDE Spring 2009 • Question 10

  1. Find the first term of the asymptotic representation of \[ n!=\int _0^\infty \exp (-t)t^{a-1}\,dt \] for large \(n\). (This approximation is called Stirling’s formula.)
  2. What is the order of the error term and how can this be rigorously justified? (Invoke the appropriate theorem.)

Raw LaTeX

\begin{enumerate}
\item[(a)] Find the first term of the asymptotic representation of
\[
  
  n!=\int_0^\infty \exp(-t)t^{a-1}\,dt
\]
for large \(n\). (This approximation is called Stirling's formula.)

\item[(b)] What is the order of the error term and how can this be rigorously justified? (Invoke
the appropriate theorem.)
\end{enumerate}

Topic Tags

Adjoint Operators and Riesz Representation Linear Programming and Optimization Low-Rank Approximation Real Integral Evaluation by Complex Methods