1931/06/01 by E. T. Whittaker · 2 citations
Mathematics · #Numerical methods for differential equations #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · pdf · doi:10.1017/s0013091500007768
openalex publication_date 1931/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
It is well known that in many cases the solutions of a linear differential equation can be expressed as definite integrals, different solutions of the same equation being represented by integrals which have the same integrand, but different paths of integration. Thus, the various solutions of the hypergeometric differential equation can be represented by integrals of the type the path of integration being (for one particular solution) a closed circuit encircling the point t = 0 in the positive direction, then the point t = 1 in the positive direction, then the point t = 0 in the negative direction, and lastly the point t = 1 in the negative direction; or (for another particular solution) an arc in the t -plane joining the points t = 1 and t = ∞.