An Expansion of the Gegenbauer Polynomial (Cn superscript mu)(xy).
Abstract
An expansion of the Gegenbauer polynomial (Cn superscript mu)(xy) in an orthogonal series in the polynomials (Ck superscript lambda)(x) with coefficients depending on y is derived. The coefficients of (Ck superscript lambda)(x) in the expansion are derived in a form that, by inspection, shows them to be positive for y > 1 and mu > or = lambda > or = 0. A limiting form for these expansion coefficients is also derived. This limiting form, together with an apparently new formula of Mehler-Heine type, is shown to imply Sonine's second finite integral. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 25, 1982
- Accession Number
- ADA113639
Entities
People
- Roy L. Streit
Organizations
- Naval Underwater Systems Center