Recursive formulas for sums of squares and sums of triangular numbers

2011/06/20 by Mohamed El Bachraoui, Bachraoui, Mohamed El
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1106.3952

9 pages

openalex publication_date 2011/06/20 · arxiv created 2011/06/22 · arxiv updated 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of the coefficients of some infinite products.

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