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An approximation to Appell's hypergeometric function F2 by branched continued fraction.
- Source :
- Dolomites Research Notes on Approximation; 2024, Vol. 17 Issue 1, p22-31, 10p
- Publication Year :
- 2024
-
Abstract
- Appell's functions F<subscript>1</subscript>-F<subscript>4</subscript> turned out to be particularly useful in solving a variety of problems in both pure and applied mathematics. In literature, there have been published a significant number of interesting and useful results on these functions. In this paper, we prove that the branched continued fraction, which is an expansion of ratio of hypergeometric functions F<subscript>2</subscript>converges uniformly to a holomorphic function of two variables on every compact subset of some domain of C²; and that this function is an analytic continuation of such ratio in this domain. As a special case of our main result, we give the representation of hypergeometric functions F<subscript>2</subscript> by a branched continued fraction. To illustrate this, we have given some numerical experiments at the end. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20356803
- Volume :
- 17
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Dolomites Research Notes on Approximation
- Publication Type :
- Academic Journal
- Accession number :
- 177499823