Lec-12. Central Difference Interpolation-III | Stirling's Interpolation | Bessel's Interpolation

In this lecture, we continue our study of central difference interpolation by deriving two of the most powerful and widely used central formulas: Stirling’s Formula and Bessel’s Formula. We examine how these formulas are formed by taking arithmetic means of Gauss's forward and backward formulas to yield maximum accuracy near the center of a table. In this lecture, you will learn: The mathematical motivation behind Stirling's and Bessel's central difference formulas Complete step-by-step derivation of Stirling's Interpolation Formula (mean of Gauss's Forward and Backward formulas) Complete step-by-step derivation of Bessel's Interpolation Formula Range of best applicability: when to choose Stirling's formula (for u between -0.25 and +0.25) vs. Bessel's formula (for u between 0.25 and 0.75) Key comparison and theoretical summary of all central interpolation formulas Useful For: B.Sc. Mathematics, B.Tech / BE Engineering Mathematics, BCA/MCA, M.Sc. Mathematics, and competitive examinations such as CSIR NET and GATE. Don't forget to Like, Share, and Subscribe to follow the complete Numerical Analysis course playlist!