Accession Number : ADA113639

Title :   An Expansion of the Gegenbauer Polynomial (Cn superscript mu)(xy).

Descriptive Note : Technical rept.,

Corporate Author : NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB

Personal Author(s) : Streit,Roy L

PDF Url : ADA113639

Report Date : 25 Mar 1982

Pagination or Media Count : 15

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)

Descriptors :   *Polynomials, Theorems, Bessel functions, Chebyshev polynomials, Formulations, Coefficients

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE