Asymptotics & Stirling’s Approximation

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Presentation transcript:

Asymptotics & Stirling’s Approximation Mathematics for Computer Science MIT 6.042J/18.062J Asymptotics & Stirling’s Approximation Copyright © Albert Meyer, 2002. Prof. Albert Meyer & Dr. Radhika Nagpal

Factorial defines a product: Stirling’s Formula Factorial defines a product: Turn product into a sum taking logs:

bound by integral method Stirling’s Formula bound by integral method …

Integral method to bound ln(n!) Stirling’s Formula Integral method to bound ln(n!)

Stirling’s Formula n!  (n/e)n n! (n/e)n = 0 lim n

Asymptotic Notation f(n) = O(g(n)) g(x) +c f(x) n0

Defs 7.1,7.2,7.3.7.7 from ln6 on separate slides