TY - JOUR
AU - WILLIAMS, M. H.
AB - A pair of algebraic recursion relations are given which generate inverses for a class of integral and integro-differential equations of the form∫-11dtk(t-x)φ(t)=g(x)The two fundamental solutions of the equation are assumed to be given by expansions in Jacobi polynomials with the weight function (1−x)α (1+x)β. The inverse kernel is then evaluated in terms of elementary functions, from which the solution for any g can be found by a single quadrature. For polynomial g the quadrature is performed analytically and the solution expressed in terms of Jacobi polynomials of the second kind.
TI - The Inversion of Singular Integral Equations by Expansion in Jacobi Polynomial†
JF - IMA Journal of Applied Mathematics
DO - 10.1093/imamat/25.4.413
DA - 1980-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/the-inversion-of-singular-integral-equations-by-expansion-in-jacobi-oToS7b0s0l
SP - 413
EP - 426
VL - 25
IS - 4
DP - DeepDyve
ER -