2,674 research outputs found
Large Parameter Cases of the Gauss Hypergeometric Function
We consider the asymptotic behaviour of the Gauss hypergeometric function
when several of the parameters a, b, c are large. We indicate which cases are
of interest for orthogonal polynomials (Jacobi, but also Krawtchouk, Meixner,
etc.), which results are already available and which cases need more attention.
We also consider a few examples of 3F2-functions of unit argument, to explain
which difficulties arise in these cases, when standard integrals or
differential equations are not available.Comment: 21 pages, 4 figure
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related
to continued fraction expansions is summarized and an attempt is made to
describe the influence of Stieltjes' ideas and work in research done after his
death, with an emphasis on the theory of orthogonal polynomials
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