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<p>The method of brackets originated from the so-called negative dimension approach for evaluating definite integrals arising in Feynman diagrams. Its fundamental concept, still heuristic, identifies a bracket with a divergent integral. The method converts the integral into a bracket series and prescribes a concise set of rules for its evaluation. In this work we present a ten-variable monstrous integral that combines Bessel functions, polylogarithms, and the exponential integral, and we evaluate it exactly by means of the method of brackets. This example illustrates the flexibility and power of the technique.</p>

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A monstrous integral

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月5日

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  • Ivan Gonzalez,
  • John Lopez Santander,
  • Victor H. Moll,
  • Daniel Salinas-Arizmendi

摘要

The method of brackets originated from the so-called negative dimension approach for evaluating definite integrals arising in Feynman diagrams. Its fundamental concept, still heuristic, identifies a bracket with a divergent integral. The method converts the integral into a bracket series and prescribes a concise set of rules for its evaluation. In this work we present a ten-variable monstrous integral that combines Bessel functions, polylogarithms, and the exponential integral, and we evaluate it exactly by means of the method of brackets. This example illustrates the flexibility and power of the technique.