1918/06/01 by E. T. Whittaker · 2 citations
Mathematics · #Differential Equations and Boundary Problems #Algebraic and Geometric Analysis #Mathematical functions and polynomials
paper · doi:10.1098/rspa.1918.0024
openalex publication_date 1918/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/21
Abstract The present communication is concerned with integral-equations of Abel’s type ∫0x ϕ (s) k (x - s) ds = f(x), (1) and of Poisson’s type ϕ (x) + ∫0x ϕ (s) k (x - s) ds = f(x), (2) where k (x) is a given function called the nucleus, f(x) is also a given function, and ϕ(x) is the unknown function which is to be determined. The object of the work is to obtain solutions of these equations in forms which can be made the basis of numerical calculation.