The sum of the r'th roots of first n natural numbers and new formula for factorial

2012/04/04 by Snehal M. Shekatkar, Snehal Shekatkar, Shekatkar, Snehal · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.1204.0877

openalex publication_date 2012/04/04 · arxiv created 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Using the simple properties of Riemman integrable functions, Ramanujan's formula for sum of the square roots of first n natural numbers has been generalized to include r'th roots where r is any real number greater than 1.As an application we derive formula that gives factorial of positive integer n similar to Stirling's formula.

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• Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series

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