Scholarlink

<p>An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geometric approach reveals the role played by the symmetries of the summation domain in the complex plane induced by the multisection technique. The second approach, based on generating functions, allows us to extend Ramanujan’s identity to other special functions such as Eisenstein’s series.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The joy of multisection: elementary approaches to Ramanujan’s lacunary identities for Bernoulli numbers

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月27日

查看全文
  • Parth Chavan,
  • Christophe Vignat

摘要

An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geometric approach reveals the role played by the symmetries of the summation domain in the complex plane induced by the multisection technique. The second approach, based on generating functions, allows us to extend Ramanujan’s identity to other special functions such as Eisenstein’s series.