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A Short Proof of Knuth’s Old Sum

21 November 2024, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

We give a short proof of the well-known Knuth’s old sum and provide some general- izations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and combinatorial identities are derived.

Keywords

Knuth’s old sum
Reed Dawson identity
Catalan number
Beta function
Combinatorial identity
polynomial identity.

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Version History

Nov 21, 2024 Version 1

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License

All Rights Reserved

DOI

10.33774/coe-2024-s4fjz
D O I: 10.33774/coe-2024-s4fjz [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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