- Volume 9 Issue 4
A PROOF OF STIRLING'S FORMULA
- Park, June-Sang (Department of Mathematics, Dongguk University, Kyongju 780-714)
- Published : 1994.10.01
The object of present note is to give a very short proof of Stirling's formula which uses only a formula for the generalized zeta function. There are several proofs for this formula. For example, Dr. E. J. Routh gave an elementary proof using Wallis' theorem in lectures at Cambridge ([5, pp.66-68]). We can find another proof which used the Maclaurin summation formula ([5, pp.116-120]). In , they used the Central Limit Theorem or the inversion theorem for characteristic functions. In , pp. Diaconis and D. Freeman provided another proof similarly as in . J. M. Patin  used the Lebesgue dominated convergence theorem.