dc.contributor.author |
Jooste, Alta
|
|
dc.contributor.author |
Njionou Sadjang, P.
|
|
dc.contributor.author |
Koepf, W.
|
|
dc.date.accessioned |
2017-04-07T09:49:26Z |
|
dc.date.issued |
2017-03 |
|
dc.description.abstract |
Zeilberger’s celebrated algorithm finds pure recurrence relations (w. r. t. a single variable) for hypergeometric
sums automatically. However, in the theory of orthogonal polynomials and special functions,
contiguous relations w. r. t. several variables exist in abundance. We modify Zeilberger’s algorithm to
generate unknown contiguous relations that are necessary to obtain inner bounds for the extreme zeros
of orthogonal polynomial sequences with 3F2 hypergeometric representations. Using this method, we
improve previously obtained upper bounds for the smallest and lower bounds for the largest zeros of
the Hahn polynomials and we identify inner bounds for the extreme zeros of the Continuous Hahn and
Continuous Dual Hahn polynomials. Numerical examples are provided to illustrate the quality of the
new bounds.
Without the use of computer algebra such results are not accessible. We expect our algorithm to be
useful to compute useful and new contiguous relations for other hypergeometric functions. |
en_ZA |
dc.description.department |
Mathematics and Applied Mathematics |
en_ZA |
dc.description.embargo |
2018-09-30 |
|
dc.description.librarian |
hb2017 |
en_ZA |
dc.description.sponsorship |
The first author would like to thank Alexander von Humboldt Foundation and TWAS for rewarding
an AGNES Grant for Junior Researchers 2014, as well as TWAS and DFG for sponsoring a
research visit at the Institute of Mathematics of the University of Kassel in 2016 (reference KO
1122/12-1). The second author would like to thank TWAS and DFG for sponsoring a research
visit at the Institute of Mathematics of the University of Kassel in 2015 (reference 3240278140). |
en_ZA |
dc.description.uri |
http://www.tandfonline.com/loi/gitr20 |
en_ZA |
dc.identifier.citation |
A. Jooste, P. Njionou Sadjang & W. Koepf (2017) Inner bounds for the extreme
zeros of 3F2 hypergeometric polynomials, Integral Transforms and Special Functions, 28:5, 361-373, DOI: 10.1080/10652469.2017.1297439. |
en_ZA |
dc.identifier.issn |
1065-2469 (print) |
|
dc.identifier.issn |
1476-8291 (online) |
|
dc.identifier.other |
10.1080/10652469.2017.1297439 |
|
dc.identifier.uri |
http://hdl.handle.net/2263/59716 |
|
dc.language.iso |
en |
en_ZA |
dc.publisher |
Taylor and Francis |
en_ZA |
dc.rights |
© 2017 Informa UK Limited, trading as Taylor & Francis Group. This is an electronic version of an article published in Integral Transforms and Special Functions , vol. 28, no. 5, pp. 361-373, 2017. doi : 10.1080/10652469.2017.1297439. Integral Transforms and Special Functions is available online at : http://www.tandfonline.comloi/gitr20. |
en_ZA |
dc.subject |
Orthogonal polynomials |
en_ZA |
dc.subject |
Extreme zeros |
en_ZA |
dc.subject |
Bounds for zeros |
en_ZA |
dc.subject |
Recurrence relations |
en_ZA |
dc.title |
Inner bounds for the extreme zeros of 3F2 hypergeometric polynomials |
en_ZA |
dc.type |
Postprint Article |
en_ZA |