Stirling formula of interpolation |  

Hello Students !
today we will discuss about the new technique to find the central diffrence
called as stirlings technique of interpolation
(stirling formula of central diffrence )
it is basically the mean of gauss forward and gauss backward interpolation formulas known as stirling technique of interpolation
The Stirling formula, also known as Stirling's interpolation formula, is a method for approximating the value of a function at a given point using the values of the function at nearby points. It is a powerful tool for interpolation and is widely used in numerical analysis.
The Stirling formula is given by:
f(x) = f₀ + (x-x₀) f'[x₀] + (x-x₀)(x-x₁) f''[x₀,x₁] / 2! + (x-x₀)(x-x₁)(x-x₂) f'''[x₀,x₁,x₂] / 3! + ...
where:
- f(x) is the value of the function at the point x
- f₀ is the value of the function at the point x₀
- f'[x₀] is the first derivative of the function at the point x₀
- f''[x₀,x₁] is the second derivative of the function at the points x₀ and x₁
- f'''[x₀,x₁,x₂] is the third derivative of the function at the points x₀, x₁, and x₂
- x₀, x₁, x₂, ... are the nearby points
The Stirling formula is a generalization of the Taylor series expansion and is useful for approximating the value of a function at a given point when the function values at nearby points are known.
Note that the Stirling formula is not the same as the Stirling approximation, which is a method for approximating the factorial function.
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