A Generalization of Ultraspherical Polynomials.

reportActive / Technical Report | Accession Number: ADA060664 | Open PDF

Abstract:

Some old polynomials of L. J. Rogers are orthogonal. Their weight function is given. The connection coefficient problem, which Rogers solved by guessing the formula and proving it by induction, is derived in a natural way and some other formulas are obtained. These polynomials generalize zonal spherical harmonics on spheres and include as special cases polynomials that are spherical functions on rank one spaces over reductive p-adic groups. A limiting case contains some Jacobi polynomials studied by Hylleraas that arose in work on the Yukawa potential. Author

Author(s):
Askey, Richard ; Ismail, Mourad E. -h.
Author Organization(s):
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Descriptive Note:
Summary rept.,
Pagination:
0032

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
MRC-TSR-1851
Contract/Grant Number(s):
DAAG29-75-C-0024, NSF-MPS75-06687
 Subject Terms
Joint Capability Areas:
JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_1.2.3_Educating
Modernization Areas:
Fully Networked C3
Communities of Interest:
C4I
Descriptor(s):
*HARMONIC ANALYSIS, *HYPERGEOMETRIC FUNCTIONS, NUCLEAR FORCES(MILITARY), WEIGHTING FUNCTIONS, SOLUTIONS(GENERAL), POLYNOMIALS, ORTHOGONALITY, LEGENDRE FUNCTIONS
Field(s)/Group(s):
Statistics and Probability
Keyword(s):
*Spherical harmonics, Yukawa potential
Report Date:
1978 May 01