F.J. van de Bult
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3 records found
1
Conference paper
(2021)
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Sayra Ranjha, Vera Hoveling, Beryl Van Gelderen, Fokko Van De Bult, Dennis Horst Van Der Den Ouden, Christophe Smet, Marijn Roelvink, Ilse Bakker
We present our short series of interactive animations on directional derivatives and level curves. This visualisation was developed for students of first-year mathematics courses at the Delft University of Technology. The interactive animation is an animated video that can be interacted with while it is paused or playing. The user can change, for example, the function that is plotted, drag points of interest or change the angle of the camera to explore the scene.
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We present our short series of interactive animations on directional derivatives and level curves. This visualisation was developed for students of first-year mathematics courses at the Delft University of Technology. The interactive animation is an animated video that can be interacted with while it is paused or playing. The user can change, for example, the function that is plotted, drag points of interest or change the angle of the camera to explore the scene.
These lecture notes discuss some of the basics of elliptic hypergeometric functions. These are fairly recent generalizations of ordinary hypergeometric functions. In this chapter we first discuss both ordinary hypergeometric functions and elliptic functions, as you need to know both to define elliptic hypergeometric series. We subsequently discuss some of the important properties these series satisfy, in particular we consider the biorthogonal functions found by Spiridonov and Zhedanov, both with respect to discrete and continuous measure. In doing so we naturally encounter the most important evaluation and transformation formulas for elliptic hypergeometric series, and for the associated elliptic beta integral.
...
These lecture notes discuss some of the basics of elliptic hypergeometric functions. These are fairly recent generalizations of ordinary hypergeometric functions. In this chapter we first discuss both ordinary hypergeometric functions and elliptic functions, as you need to know both to define elliptic hypergeometric series. We subsequently discuss some of the important properties these series satisfy, in particular we consider the biorthogonal functions found by Spiridonov and Zhedanov, both with respect to discrete and continuous measure. In doing so we naturally encounter the most important evaluation and transformation formulas for elliptic hypergeometric series, and for the associated elliptic beta integral.
Limits of elliptic hypergeometric biorthogonal functions
To Dick Askey on the occasion of his 80th birthday
The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the -Askey scheme of basic hypergeometric orthogonal polynomials. We aim to achieve this by looking at the limits as p -> 0 of the elliptic hypergeometric biorthogonal functions from Spiridonov (2003), with parameters which depend in varying ways on p. As a result we get 38 systems of biorthogonal functions with for each system at least one explicit measure for the bilinear form. Amongst these we indeed recover the q-Askey scheme. Each system consists of (basic hypergeometric) rational functions or polynomials.
...
The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the -Askey scheme of basic hypergeometric orthogonal polynomials. We aim to achieve this by looking at the limits as p -> 0 of the elliptic hypergeometric biorthogonal functions from Spiridonov (2003), with parameters which depend in varying ways on p. As a result we get 38 systems of biorthogonal functions with for each system at least one explicit measure for the bilinear form. Amongst these we indeed recover the q-Askey scheme. Each system consists of (basic hypergeometric) rational functions or polynomials.