Karaji's L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula

Year 2021, Volume: 13 Issue: 1, 122 - 128, 30.06.2021

Hossein Teimoori Faal

https://doi.org/10.47000/tjmcs.717074

https://izlik.org/JA44JN35SN

Abstract

In this paper, we first review two folkloric summation techniques
due to two Islamic medieval scholars Karaji and Ibn al-Haytham by emphasizing on their higher-dimensional extensions. We also include several interesting examples of algebraic identities obtained
form the generalized Ibn al-Haytham formulas and Karaji's
L-summing method. Finally, we
will also show the interplay between these two different methods
of summation.

Keywords

Karaji , the generalized Ibn al-Haytham formula , summation techniques , sums of powers , harmonic numbers

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