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

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

References

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