Barnes? beta integral
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1: 5.13 Integrals
Barnes’ Beta Integral
…2: 16.15 Integral Representations and Integrals
§16.15 Integral Representations and Integrals
… ►3: 35.8 Generalized Hypergeometric Functions of Matrix Argument
Euler Integral
►§35.8(v) Mellin–Barnes Integrals
►Multidimensional Mellin–Barnes integrals are established in Ding et al. (1996) for the functions and of matrix argument. …These multidimensional integrals reduce to the classical Mellin–Barnes integrals (§5.19(ii)) in the special case . …4: Bibliography N
5: Errata
For consistency we have replaced by .
The statements “If and are real” and “If and are not both real” have been further clarified (suggested by Alan Barnes on 2021-03-26).
The descriptions for the paths of integration of the Mellin-Barnes integrals (8.6.10)–(8.6.12) have been updated. The description for (8.6.11) now states that the path of integration is to the right of all poles. Previously it stated incorrectly that the path of integration had to separate the poles of the gamma function from the pole at . The paths of integration for (8.6.10) and (8.6.12) have been clarified. In the case of (8.6.10), it separates the poles of the gamma function from the pole at for . In the case of (8.6.12), it separates the poles of the gamma function from the poles at .
Reported 2017-07-10 by Kurt Fischer.
Two corrections have been made in this paragraph. First, the correct range of the initial displacement is . Previously it was . Second, the correct period of the oscillations is . Previously it was given incorrectly as .
Reported 2014-05-02 by Svante Janson.
Originally the term was incorrectly stated as .
Reported 2013-08-01 by Gergő Nemes and subsequently by Nick Jones on December 11, 2013.