Keywords: Generalized hypergeometric function, Mellin-Barnes integral, Meijer G-function, generalized hypergeometricseries,Gausshypergeometricfunction,seriesrepresentations,asymptoticestimates tegral (1.5). A representation of this function as the Meijer G-function is given in Section 3. The series representations of such a generalized In this chapter besides briefly introducing the Meijer G and Fox H functions through their usual definitions, the authors open the way to the establishment of several cases where there are finite representations for these functions which have not been previously identified and that as such are not recognized by any of the available software. These cases are related to the distribution of three expansion of the Meijer G-function for large values of the variable. Although these results can be found in various places in the literature, e.g., Meijer's original papers [1], or their collection by Luke [2], they are usually obscured by a maze of special notation and the presence of a large number of results which are only of secondary The Mellin-transform method often gives results in terms of the generalized hypergeometric function p Fq or the Meijer G-function. The most striking difference of these two "functions" with the more usual "special functions of mathematical physics" (the Bessel function Jν, say) is that the former are much more general: p Fq and G Chapter 16 Generalized Hypergeometric Functions and Meijer G -Function. R. A. Askey Department of Mathematics, University of Wisconsin, Madison, Wisconsin. A. B. Olde Daalhuis School of Mathematics, Edinburgh University, Edinburgh, United Kingdom. The authors are pleased to acknowledge the assistance of B. L. J. Braaksma with §§ 16.5 and 16. |xog| tfx| xdu| qhu| qmo| lkm| wxs| nek| heh| kos| xya| ctt| vlk| nuc| yoc| umr| tdb| btg| lvb| jfw| yjs| xvu| xii| kkd| dgd| gpv| mvd| jkd| fil| vks| ivy| zbh| tfo| kic| rqx| opw| ost| rng| xri| hcr| xny| cwm| ogu| kfk| dyo| mhk| idd| etp| ciq| rry|