## Finite Calculus: A Tutorial for Solving Nasty Sums

A precise calculation: a guide for solving his Nasty. David Gleich … In this tutorial I will first explain the need for an accurate calculation ….

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**Finite Calculus: A Tutorial for Solving Nasty Sums**, contents:

- How to Evaluate ân x=1 x2?
- 2 The Computational Cost of Gaussian Elimination
- 3 The Finite Calculus

3.1 Discrete Derivative

3.2 The Indefinite Sum and the Discrete Anti-Derivative

3.3 Helpful Finite Calculus Theorems - 4 Making Finite Calculus Useful: Stirling and His Numbers

4.1 Stirling Numbers (of the Second Kind)

4.2 Proving the Theorem

4.3 Computing Stirling Numbers - 5 Examples Galore.

5.1 ân x=1 x2

5.2 A Double Sum

5.3 Average Codeword Length - 6 Conclusion

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