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The use of two-point Taylor expansions in singular one-dimensional boundary value problems I
(Elsevier, 2018)
info:eu-repo/semantics/article,
We consider the second-order linear differential equation (x + 1)y′′ + f(x)y′ + g(x)y = h(x) in
the interval (−1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed
Dirichlet-Neumann). The ...
Convergent and asymptotic methods for second-order difference equations with a large parameter
(Springer, 2018)
info:eu-repo/semantics/article,
We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find ...
Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
(Taylor & Francis, 2018)
info:eu-repo/semantics/article,
We consider the hypergeometric function 2F1(a, b; c; z) for z ∈ C \ [1,∞). For Ra ≥ 0, we derive a convergent expansion of 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly ...
Uniform representation of the incomplete beta function in terms of elementary functions
(Kent State UniversityJohann Radon Institute (RICAM), 2018)
info:eu-repo/semantics/article,
We consider the incomplete beta function Bz(a, b) in the maximum domain of analyticity of its three variables: a, b, z ∈ C, −a /∈ N, z /∈ [1, ∞). For <b ≤ 1 we derive a convergent expansion of z−aBz(a, b) in terms of the ...