Nico M. Temme

Learn More
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 given(More)
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 functions(More)
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 that(More)
Integral representations are considered of solutions of the Airy differential equation w ′′−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 second(More)
Integral representations are considered of solutions of the inhomogeneous Airy differential equation w′′ − z w = ±1/π. 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 descent(More)
Each family of Gauss hypergeometric functions fn = 2F1(a + ε1n, b + ε2n; c + ε3n; z), for fixed εj = 0,±1 (not all εj equal to zero) satisfies a second order linear difference equation of the form Anfn−1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different εj values) can be(More)
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 the(More)
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. We(More)