Coupling of the Legendre polynomials with kernels $|x-y|^α$ and $\ln|x-y|$
| dc.creator | Sadov, S. | |
| dc.date | 2003-10-06 | |
| dc.date.accessioned | 2026-07-07T05:01:38Z | |
| dc.date.available | 2026-07-07T05:01:38Z | |
| dc.description | Double integrals that represent matrix elements of the power and logarithmic potentials in the Legendre polynoiomial basis on [-1,1] are found in a closed form. Several proofs are given, which involve different special functions and identities. A connection of the new formulae and Whipple's hypergeometric summation formula is shown. | |
| dc.description | 23 pp. LaTeX, Preprint of the Keldysh Institute for Applied Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0310063 | |
| dc.identifier | http://arxiv.org/abs/math/0310063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68748 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33C20; 45H05 | |
| dc.title | Coupling of the Legendre polynomials with kernels $|x-y|^α$ and $\ln|x-y|$ | |
| dc.type | text |