
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 MehlerHeine 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