Department of Decision Sciences

Prof KH Jordaan

College of Economic and Management Sciences
School of Economic and Financial Sciences
Department: Decision Sciences
Professor
Tel: 012 433 4620
E-mail: jordakh@unisa.ac.za

Qualifications

  • BSc (UP)
  • H.Dip.Ed. (UP)
  • BSc(Hons) (WITS)
  • MSc (UP)
  • PhD (WITS)

NRF Rating

B3

Currently teaching

  • Financial Modelling
  • Stochastic Calculus
  • Masters and PhD supervisor

Fields of academic interests

  • Financial Mathematics
  • Mathematical Analysis
  • Approximation Theory

Field of Specialisation

My research is in the area of Mathematics and my research interests are

  • Special functions;
  • Classical and semi-classical orthogonal polynomials;
  • Asymptotic analysis.

Journal articles

  • P A Clarkson and K. Jordaan, Generalised Airy polynomials, J. Phys. A: Math. Theor. 54(18) (2021) 185202 (28pp). DOI: 10.1088/1751-8121/abf019
  • P A Clarkson, & K Jordaan, A generalised Sextic Freud Weight, Integral Transforms and Special Functions, 32(5-8) (2021), 458-482. DOI: 10.1080/10652469.2020.1798949
  • K Jordaan, Zeros of orthogonal polynomials, Tutorials, Schools, and Workshops in the Mathematical Sciences: Orthogonal Polynomials, Springer Nature; Birkhäuser, Chapter 17, 2020. DOI: 10.1007/978-3-030-36744-2_17
  • K Jordaan, Properties of certain classes of Semiclassical Orthogonal Polynomials, Tutorials, Schools, and Workshops in the Mathematical Sciences: Orthogonal Polynomials     Springer Nature; Birkhäuser, Chapter 18, 2020. DOI: 10.1007/978-3-030-36744-2_18
  • P P Kar, K Jordaan, P Gochhayat, & M K Nangho, Quasi-orthogonality and zeros of 2Φ2 and 3Φ2 polynomials, Journal of Computational and Applied Mathematics, 377 (2020), 1-13. DOI: 10.1016/j.cam.2020.112910
  • M Kenfack Nangho, & K Jordaan, A characterization of Askey-Wilson polynomials, Proceedings of the American Mathematical Society, 147(6) (2019). DOI: 2465-2480 10.1090/proc/14317
  • M Kenfack Nangho, & K Jordaan, Structure relations of classical orthogonal polynomials of the quadratic and q-quadratic variable, SIGMA, 14 (2018) 26 pages. DOI: 10.3842/SIGMA.2018.126
  • K Driver, & K Jordaan, Zeros of Jacobi polynomials Pn(α,β) , -2<α,β<-1, Numerical Algorithms, 79 (4) (2018), 1075-1085. DOI: 10.1007/s11075-018-0474-6
  • PA Clarkson, & K Jordaan, Properties of generalized Freud polynomials, Journal of Approximation Theory, 225 (2018), 148-175. DOI: 10.1016/j.jat.2017.10.001
  • K Driver, & K. Jordaan, Zeros of quasi-orthogonal Jacobi polynomials, SIGMA, 12 (2016), 042, 13 pages. DOI: 10.3842/SIGMA.2016.042
  • PA Clarkson, K Jordaan, & A Kelil, A generalized Freud weight, Studies in Applied Mathematics, 136 (2016), 288-320. DOI: 10.1111/sapm.12105
  • SJ Johnston, A Jooste, & K Jordaan, Quasi-orthogonality of some hypergeometric polynomials, Integral transforms and Special Functions, 27 (2) (2016), 111-125. DOI: 10.1080/10652469.2015.1098635
  • P Gochhayat, K Jordaan, K Raghavendar, & A Swaminathan, Interlacing properties and bounds for zeros of 2Φ1 hypergeometric and little q-Jacobi polynomials, Ramanujan Journal, 40 (2016), 45-62. DOI:10.1007/s11139-015-9709-5
  • SJ Johnston, & K Jordaan, Quasi-orthogonality and real zeros of some 2F2 and 3F2 polynomials. Applied Numerical Mathematics, 90 (2015) 1-8. DOI: 10.1016/j.apnum.2014.11.008
  • K Jordaan, H Wang, & J Zhou, Monotonicity of zeros of polynomials orthogonal with respect to an even weight function, Integral Transforms and Special Functions. 25 (9) (2014), 721-729. DOI: 10.1080/10652469.2014.904303
  • K Jordaan, & A Jooste, Bounds for zeros of Meixner and Kravchuk polynomials, London Mathematical Society Journal of Computation and Mathematics, 17 (1) (2014) 47-57. DOI: 10.1112/S1461157013000260
  • K Jordaan, & F Toókos, Orthogonality and asymptotics of Pseudo-Jacobi polynomials for non-classical parameters, Journal of Approximation Theory, 178 (2014), 1-12. DOI: 10.1016/j.jat.2013.10.003
  • PA Clarkson, & K Jordaan, The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation, Constructive Approximation 39(1) (2014), 223-254. DOI: 10.1007/s00365-013-9220-4
  • A Jooste, K Jordaan, & F Toókos, On the zeros of Meixner polynomials, Numerische Mathematik, 124 (2013), 57-71. DOI: 10.1007/s00211-012-0504-6
  • K Driver, & K Jordaan, Inequalities for extreme zeros of some classical orthogonal and q-orthogonal polynomials, Mathematical Modelling of Natural Phenomena, 8(1) (2013), 48-59. DOI: 10.1051/mmnp/20138102.
  • D Dominici, SJ Johnston, & K Jordaan, Real Zeros of 2F1 Hypergeometric Polynomials, Journal of Computational and Applied Mathematics. 247 (2013), 152–161. DOI: 10.1016/j.cam.2012.12.024
  • K Driver, & K Jordaan, Bounds for extreme zeros of some classical orthogonal polynomials, Journal of Approximation Theory, 164 (2012), 1200-1204. DOI: 10.1016/j.jat.2009.05.010
  • K Driver, A Jooste, K Jordaan, Stieltjes interlacing of zeros of Jacobi polynomials from different sequences, Electronic Transactions on Numerical Analysis, 38 (2011), 317-326. Available here
  • D Dominici, K Driver, & K Jordaan, Polynomial solutions of differential-difference equations, Journal of Approximation Theory, 163 (2011), 41-48. DOI: 10.2016/j.jat.2009.05.010
  • A Beardon, K Driver, K Jordaan, Zeros of polynomials embedded in an orthogonal sequence, Numerical Algorithms, 57 (2011), 399-403. DOI: 10.1007/s11075-010-9435-4
  • K Driver, & K Jordaan, Stieltjes interlacing of zeros of Laguerre polynomials from different sequences, Indagationes Mathematicae, 21 (2011), 204–211. DOI: 10.1016/j.indag.2011.04.003
  • K Jordaan, F Toókos, Mixed relations and interlacing of the zeros of some q-orthogonal polynomials from different sequences, Acta Mathematica Hungarica, 128 (1-2) (2010), 150-164. DOI: 10.1007/s10474-010-9176-9
  • K Driver, K Jordaan, N Mbuyi, On the interlacing of zeros of linear combinations of Jacobi polynomials from different sequences, Quaestiones Mathematicae, 32(1) (2009), 47-54. DOI: 10.2989/QM.2009.32.1.5.707
  • K Jordaan, F Toókos, Interlacing theorems for the zeros of some orthogonal polynomials from different sequences, Applied Numerical Mathematics, 59 (8) (2009), 2015-2022. DOI: 10.1016/j.apnum.2009.04.002
  • K Driver, K Jordaan, N Mbuyi, Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences, Applied Numerical Mathematics, 59 (2009), 2424-2429. DOI: 10.1016/j.apnum.2009.04.007
  • K Jordaan, F Toókos, Convexity of the zeros of some orthogonal polynomials and related functions, Journal of Computational and Applied Mathematics, 233 (2009), 762-767. DOI: 10.1016/j.cam.2009.02.045
  • K Driver, K Jordaan, Zeros of linear combinations of Laguerre polynomials from different sequences, Journal of Computational and Applied Mathematics, 233 (2009), 719-722. DOI: 10.1016/j.cam.2009.02.091
  • K Driver, K Jordaan, N Mbuyi, Interlacing of the zeros of Jacobi polynomials with different parameters, Numerical Algorithms, 49 (2008), 143-152. DOI: 10.1007/s11075-008-9162-2
  • K Driver, K Jordaan, Separation theorems for the zeros of certain hypergeometric polynomials, Journal of Computational and Applied Mathematics, 199 (2007), 48-55. DOI: 10.1016/j.cam.2005.05.039
  • K Driver, K Jordaan,  A Martínez-Finkelshtein, Pólya frequency sequences and real zeros of some 3F2 polynomials, Journal of Mathematical Analysis and Applications, 332 (2007), 1045-1055. DOI: 10.1016/j.jmaa.2006.10.080
  • K Driver, K Jordaan, Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials, Numerische Mathematik, 107 (2007), 615-624. DOI: 10.1007/s00211-007-0100-3
  • K Driver, K Jordaan, Zeros of 3F2(-n,b,c;d,e;z) polynomials, Numerical Algorithms, 30 (3,4), (2002), 323-333. DOI: 10.1023/A:1020126822435     
  • K Driver, K Jordaan, Asymptotic zero distribution of a class of 3F2 hypergeometric functions, Indagationes Mathematicae, New Series, 14 (3,4), (2003),  319-327. DOI: 10.1016/S0019-3577(03)90049-8
  • K Driver, K Jordaan, Convergence of ray sequences of Padé  approximants for 2F1(a,1;c;z), c>a>0, Quaestiones Mathematicae, 25 (2002), 1-7.  DOI: 10.2989/16073600209486038
  • K Driver, & K Jordaan, Zeros of the hypergeometric polynomial F(-n, b; c; z) ,  Algorithms for Approximation IV, Proceedings of the 2001 International Symposium, (2002),  436-445. https://arxiv.org/abs/0812.0708

Paper presentations

More than 45 invited and contributed talks given at national and international conferences and seminar series in Austria, Brazil, Cameroon, Denmark, Finland, France, Germany, Hong Kong, Hungary, India, Netherlands, Portugal, Spain, Uruguay, UK and USA, including the following plenary/keynote talks:

  • Generalised higher order Freud polynomials, Online network research group international seminar series on Orthogonal Polynomials (OPSFOTA), Special Functions and Operator Theory and Applications, 15:00 BST, 29 March 2021.
  • A characterisation of Askey-Wilson polynomials and the indeterminate moment problem associated with a limiting case, Complex Analysis video seminars (CAvid), 14:00 UTC, 1 December 2020.
  • Asymptotic zero distribution of generalised hypergeometric polynomials, Workshop: The complex analysis toolbox: new techniques and perspectives, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 9-13 August 2019.
  • Zeros of orthogonal polynomials, AIMS-Volkswagen Stiftung Workshop on Introduction to Orthogonal Polynomials and Applications, Douala, Cameroon, 8-12 October 2018.
  • Properties of certain classes of semi-classical orthogonal polynomials, AIMSVolkswagen Stiftung Workshop on Introduction to Orthogonal Polynomials and Applications, Douala, Cameroon, 8-12 October 2018.
  • Characterisations of orthogonal polynomials, South African Numerical and Applied Mathematics (SANUM), Stellenbosch Unviversity, South Africa, April 2018.
  • Orthogonal polynomials characterized by structure relations, International Conference on Integrable systems, discrete symmetries and orthogonal polynomials,Institute of Mathematical Sciences, Madrid, Spain, 18-22 September, 2017.
  • Lecture series on Properties of orthogonal polynomials, London Mathematical Society Research School on Orthogonal polynomials and special functions, University of Kent, UK 26-30 June, 2017.
  • Properties of some semi-classical orthogonal polynomials, VI Iberoamerican workshop on orthogonal polynomials and applications, Universidade Federal do Triângulo Mineiro Uberaba, Brazil, 9-12 May, 2017.
  • Properties of generalized Freud polynomials, International Conference on Mathematical Analysis and Applications, Indian Institute of Technology, Roorkee, India, 28 Nov-2 Dec 2016.
  • Orthogonal polynomials under modification of the measure, Workshop on Functional Analysis and its Applications, North Wwest University, South Africa, September 2015.
  • The mathematics of money, Annual congress of the Association for Mathematics Education in South Africa (AMESA), University of Limpopo. Nominated plenary speaker representing the South African Mathematical Society, 2006.

Professional positions, fellowships & awards

ACADEMIC AND SCIENTIFIC CITIZENSHIP

  • International Society for Industrial and Applied Mathematics (SIAM):
    • Membership Committee, January 2019 - December 2021.
    • Activity Group on Orthogonal Polynomials and Special Functions (SIAG-OPSF):
      • Appointed co-editor of the electronic newsletter of the SIAG OPSF: 2015–2016;
      • Nominating committee for the election of officers: Member, 2016
      • Selection committee for the prestiguous international Gabor Szegö prize: 
             Chariperson (2016/2017) Member 2014/2015; 2020/2021;
    • Member since 2009.
  • South African Mathematical Society (SAMS):
    • President 2016-2019;
    • Elected Council member for Scientific Activities 2008-2011;
    • Member since 2000.
  • South African Mathematics Foundation (SAMF):
    • Executive Director since August 2018;
    • Chairperson of the Board of Directors January 2017-July 2018;
    • Vice-Chair of the Board of Directors 2015–2016;
    • Member of the Board of Directors since 2008.
  • National Graduate Academy for Mathematical and Statistical Sciences:
    • Advisory Board member since 2020.
  • National Research Foundation (NRF):
    • NRF rating specialist committee for Mathematical Sciences:
      • Convener 2020 - Feb 2021;
      • Member 2017 - Feb 2021;
    • Advisory panel member for Mathematical sciences:
      • Competitive research grants, 2011, 2013, 2014, 2015;
      • Institutional Capacity Development Grants Thuthuka programme, 2012.
  • Department of Science and Innovation:
    • DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences Steering committee: Member 2016-2019;
    • DSI South African Basic Sciences Development Platform: member 2017-2020;

AWARDS AND OTHER SCIENTIFIC SCHOLARLY RECOGNITION

  • Academy of Sciences of South Africa: Elected member since October 2021;
  • Royal Society:  Newton Advanced Fellowship, 2018-2023;
  • International Mathematical Union: Invited observer at Executive Committee meeting, February 2020;
  • African Institute for Mathematical Sciences South Africa: Associate Research Fellow since 2015;
  • International Centre for Mathematical Sciences: Visiting researcher, 2019;
  • Isaac Newton Institute for Mathematical Sciences: By-invitation themed semester workshop plenary speaker, 2019.