On mellinbarnes integral representations for gkz hypergeometric. Asymptotics and mellinbarnes integrals, first published in, provides an account of the use and properties of a type of complex integral representation that. Asymptotics and mellinbarnes integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After the construction of a mb representation for a given feynman integral, one has a large amount of public tools at hand for their subsequent. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special. The simplest bulk action one can write down on the bruhattits tree is the free lat tice action. The hypergeometric approach to integral transforms and.
Publication date 2001 topics asymptotic expansions, mellin transform. Asymptotics and mellinbarnes integrals encyclopedia of. In mathematics, a barnes integral or mellinbarnes integral is a contour integral involving a. Asymptotics and mellinbarnes integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. A new development of the theory of the hypergeometric functions pdf. Asymptotics and mellinbarnes integrals by paris, r. Asymptotics and mellinbarnes integral pdf asymptotics and mellinbarnes integrals, first published in, provides an account of the use and properties of a type of complex integral representation. Moreover, the mellinbarnes type integrals can be understood as an. Barnes integral representation the mellin transform of a function is given by fs. These examples suggest that we might obtain a complex integral representation for the hypergeometric function 2f 1 by nding its mellin transform. Mellinbarnes integrals of higher dimension are also considered. Buy asymptotics and mellinbarnes integrals encyclopedia of mathematics and its applications on.
On convergent series representations of mellinbarnes integrals. Mar 28, 20 asymptotics and mellin barnes integrals by r. Asymptotics and mellinbarnes integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study. Kaminski is one of the first new, extended texts to be published in english since the recent advances began, and is a mixture of existing and novel techniques and applications.
The hypergeometric approach to integral transforms and convolutions. Applications of the mellinbarnes integral representation. Numerical integration of massive twoloop mellinbarnes integrals in. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of mellinbarnes integrals that. Encyclopedia of mathematics and its applications asymptotics.
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