interpolation formula ,sub topic-stirling formla

1. Prepared by-
Harsh Kothari (170120107066)
Guided by – Prof. Priya Jani
Gandhinagar Institute of Technology
SUBJECT - NSM (2140706)
TOPIC: Stirling Method

2. contents
• What is Stirling's formula
• Proof for formula
• Examples

3. STIRLING’S FORMULA
 This formula 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 will be 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)