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Stirling's formula is an interesting and useful way to approximate the factorial function, n!, for large values of n. Standard derivations require a substantial background in classical analysis, but in fact the rule can be derived in a fairly general form based on nothing more than the trapezoid rule and its error estimate. Exercise 1 Stirling's Formula Show that for all n>2, there exists a value C, 2.37 < Cn <2.501, such that n! = Cn√n (n/e)". Exercise 2

Stirling's formula is an interesting and useful way to approximate the factorial function, n!, for large values of n. Standard derivations require a substantial background in classical analysis, but in fact the rule can be derived in a fairly general form based on nothing more than the trapezoid rule and its error estimate. Exercise 1 Stirling's Formula Show that for all n>2, there exists a value C, 2.37 < Cn <2.501, such that n! = Cn√n (n/e)". Exercise 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Stirling's formula is an interesting and useful way to approximate the factorial function, n!, for large values of n. Standard derivations require a substantial background in classical analysis, but in fact the rule can be derived in a fairly general form based on nothing more than the trapezoid rule and its error estimate. Exercise 1 Stirling's Formula Show that for all n > 2, there exists a value C, 2.37 < Cn <2.501, such that n! = C₁ √n (n/e)". Exercise
Transcribed Image Text:Stirling's formula is an interesting and useful way to approximate the factorial function, n!, for large values of n. Standard derivations require a substantial background in classical analysis, but in fact the rule can be derived in a fairly general form based on nothing more than the trapezoid rule and its error estimate. Exercise 1 Stirling's Formula Show that for all n > 2, there exists a value C, 2.37 < Cn <2.501, such that n! = C₁ √n (n/e)". Exercise
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