Applications of Nörlund’s formula and linear forms for continued fractions

John Campbell () and Kwang-Wu Chen ()
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John Campbell: York University
Kwang-Wu Chen: University of Taipei

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 4, 1542-1548

Abstract: Abstract We provide a method for determining explicit symbolic evaluations for infinite families of continued fractions with quadratic partial numerators and constant partial denominators. In this manner, we obtain continued fraction identities generalizing results due to Ramanujan and Stieltjes. Our method relies on Nörlund’s formula together with generalizations of classical hypergeometric series identities due to Rakha and Rathie. We also introduce and apply a related technique concerning linear forms for continued fractions to build on the work of Dougherty-Bliss and Zeilberger related to “The Ramanujan Machine.”

Keywords: Continued fraction; Nörlund’s formula; Hypergeometric series; 11A55; 33C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00765-x

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