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1.1600144131169847160014413116984775294152416942826...
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Paul J. Nahin, <a href="https://doi.org/10.1007/978-3-030-43788-6">Inside interesting integrals</a>, Undergrad. Lecture Notes in Physics, Springer (2020), p. 135, eq. (4.3.7).
RealDigits[Sqrt[3] * Gamma[1/3]/4, 10, 120][[1]] (* Amiram Eldar, Jun 10 2024 *)
(PARI) sqrt(3) * gamma(1/3) / 4 \\ Amiram Eldar, Jun 10 2024
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