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. Theâ€¦ (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,â€¦ (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 asymmetricâ€¦ (More)

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 integralâ€¦ (More)

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 pointâ€¦ (More)

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. Certainâ€¦ (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 formâ€¦ (More)

Methods for the computation of real parabolic cylinder functions U(a, x), and V(a, x) and their derivatives are described. We give details on power series, asymptotic series, recursion andâ€¦ (More)