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Confluence expansions of the generalized hypergeometric function
KTH, Superseded Departments, Physics.
2004 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 45, no 1, 495-508 p.Article in journal (Refereed) Published
Abstract [en]

By confluencing a subset of upper and lower parameters in the generalized hypergeometric function F-P(Q)(a(1,),...,a(P),c(1),...,c(Q);z) with the variable z one obtains a lower-order hypergeometric function in the limit when the confluence parameters go to infinity. It is shown that this function is the first term in a convergent expansion in terms of functions of the same type with parameters increasing stepwise by integers nu and coefficients which are polynomials in the reciprocals of the confluence parameters. These polynomials have nonvanishing lowest degree terms whose power increases with nu. The expansion can hence be used to derive asymptotic expansions for large but finite absolute values of the confluence parameters.

Place, publisher, year, edition, pages
2004. Vol. 45, no 1, 495-508 p.
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-45718DOI: 10.1063/1.1629777ISI: 000187429200031ScopusID: 2-s2.0-0346040230OAI: diva2:453163
QC 20111101Available from: 2011-11-01 Created: 2011-10-31 Last updated: 2011-11-01Bibliographically approved

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