On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-christoffel rules, I
1997; Springer Science+Business Media; Volume: 37; Issue: 2 Linguagem: Inglês
10.1007/bf02510213
ISSN1572-9125
Autores Tópico(s)Fractional Differential Equations Solutions
ResumoThree methods, old but not so well known, transform an infinite series into a complex integral over an infinite interval. Gauss quadrature rules are designed for each of them. Various questions concerning their construction and application are studied, theoretically or experimentally. They are so efficient that they should be considered for the development of software for special functions. Applications are made to slowly convergent alternating and positive series, to Fourier series, to the numerical analytic continuation of power series outside the circle of convergence, and to ill-conditioned power series.
Referência(s)