The Barnes G-function is a special function in mathematical analysis and number theory, which generalizes the gamma function and is related to various areas such as complex analysis, combinatorics, and the theory of special functions. It was introduced by the mathematician W. R. Barnes in the early 20th century. The Barnes G-function, denoted as \( G(a; b) \), is defined for complex numbers and can be constructed from the Gamma function.
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