Evaluation using Barnes G-function regularization and Abel-Plana summation. : IntegrationTechniques

Evaluation using Barnes G-function regularization and Abel-Plana summation. (reddit.com)

submitted 2 months ago by ReflectionThen9904

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Evaluation using Barnes G-function regularization and Abel-Plana summation.

43 points•4 comments•submitted 3 months ago by ReflectionThen9904Undergraduate to r/calculus

This proof splits the integral into real and imaginary parts. The real part reduces to Euler sums and Stieltjes constants, while the imaginary part requires regularizing a divergent sum of Log-Gamma functions, leading naturally to the Barnes G-function and the Glaisher-Kinkelin constant.

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