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- U. Ebert, Manuel ArrayÃ¡s, Nico M. Temme, Ben P. Sommeijer, J. Huisman
- Bulletin of mathematical biology
- 2001

We motivate and analyse a reaction-advection-diffusion model for the dynamics of a phytoplankton species. The reproductive rate of the phytoplankton is determined by the local light intensity. The light intensity decreases with depth due to absorption by water and phytoplankton. Phytoplankton is transported by turbulent diffusion in a water column of givenâ€¦ (More)

- Nico M. Temme
- 2002

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 functionsâ€¦ (More)

- Andrew E. Noble, Nico M. Temme, William F. Fagan, Timothy H. Keitt
- Journal of theoretical biology
- 2011

We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community dynamics, while an analogous extension of Hubbell's metacommunity dynamics is deferred to an appendix. We find thatâ€¦ (More)

- Amparo Gil, Javier Segura, Nico M. Temme
- Numerical Algorithms
- 2002

Integral representations are considered of solutions of the Airy differential equation w â€²â€²âˆ’zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a secondâ€¦ (More)

- Nico M. Temme
- 2000

Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are modified to improve the asymptotic properties and to enlargeâ€¦ (More)

- Amparo Gil, Javier Segura, Nico M. Temme
- Math. Comput.
- 2001

Integral representations are considered of solutions of the inhomogeneous Airy differential equation wâ€²â€² âˆ’ z w = Â±1/Ï€. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descentâ€¦ (More)

Each family of Gauss hypergeometric functions fn = 2F1(a + Îµ1n, b + Îµ2n; c + Îµ3n; z), for fixed Îµj = 0,Â±1 (not all Îµj equal to zero) satisfies a second order linear difference equation of the form Anfnâˆ’1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different Îµj values) can beâ€¦ (More)

- Amparo Gil, Javier Segura, Nico M. Temme
- ACM Trans. Math. Softw.
- 2006

Methods for the computation of real parabolic cylinder functions <i>U</i>(<i>a</i>, <i>x</i>), and <i>V</i>(<i>a</i>, <i>x</i>) and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A combination of these methods can be used for computing parabolic cylinder functions for unrestricted values of theâ€¦ (More)

- Nico M. Temme
- 2007

REPORTRAPPORT Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters Abstract We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. Weâ€¦ (More)