Extension of Summation Formulas involving Stirling series

2016/05/16 by Raphael Schumacher, Schumacher, Raphael
Mathematics · #11B68 (Secondary) #65B15 (Primary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1605.09204

openalex publication_date 2016/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a family of rapidly convergent summation formulas for various finite sums of the form ∑_k=0^{\lfloor x\rfloor}f(k), where x is a positive real number.

Citations

• Summation of Divergent Power Series by Means of Factorial Series

Related

• Rapidly Convergent Summation Formulas involving Stirling Series
• The Generalization of Faulhaber's Formula to Sums of Arbitrary Complex Powers
• A sum up method for solving summations of the form ∑_k=n0ⁿ A_n,k and rising and falling factorial transforms
• Connecting the Stirling numbers and k-bonacci sums
• A Short Proof of Stirling's Formula