Krull's theory for the double gamma function
نویسندگان
چکیده
The Barnes’ G-function G(x) = 1/Γ2, satisfies the functional equation log G(x + 1) − log G(x) = log Γ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1)− g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.
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عنوان ژورنال:
- Applied Mathematics and Computation
دوره 218 شماره
صفحات -
تاریخ انتشار 2011