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stirling method maths
Stirling's formula provides an approximation of factorials and is derived as the average of the Gauss forward and backward interpolation formulae. It is most accurate when -1/4 < p < 1/4. The formula is f(x) = f(x0) + f'(x0)(x - x0) + (f"(x0)/2!)(x - x0)^2 + ... + (f^((n))(x0)/n!)(x - x0)^n, where f^((n))(x0) is the nth derivative of f evaluated at x0. Stirling's formula is obtained by taking the average of the Gauss forward and backward difference formulae.
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stirling method maths
- 1. Prepared by- Harsh Kothari(170120107066) Guided by – Prof. Priya Jani Gandhinagar Institute of Technology SUBJECT - NSM (2140706) TOPIC: Stirling Method
- 2. contents • What isStirling's formula • Proof for formula • Examples
- 3. STIRLING’S FORMULA Thisformula gives the average of the values obtained by Gauss forward and backward interpolation formulae. For using this formula we should have – ½ < p< ½. We can get very good estimates if - ¼ < p < ¼. The formula is: where h u x x0
- 4. Proof: Stirling’s Formula willbe obtained by taking the average of Gauss forward difference formula and Gauss Backward difference formula. We know that, from Gauss forward difference formula Also, from Gauss backward difference formula Now ,stirling formula=1/2(gauss forward formula + gauss backward formula)