Absolute and Uniform Convergence of Alternative Forms of the Prolate Spheroidal Radial Wave Functions

Journal Article · Sat Aug 17 04:00:00 EDT 2002 · Advances in Applied Mathematics, 29(2):311-327

DOI:https://doi.org/10.1016/S0196-8858(02)00015-5· OSTI ID:15010118

Jones-Oliveira, Janet B; Fischer, Hans R

A new orthonormal basis set representation of the prolate spheroidal radial and angular wave functions is presented. The embedded series solutions to a fully-coupled fluid-solid interaction continuum physics problem is defined by product sets of Legendre polynomials and modified spherical Bessel functions of the first and third kinds. We prove that the embedded series solutions analytically converge absolutely and uniformly to the exact solutions of the system of coupled continuum equations. The satisfaction of the bilinear concomitant and its utility in establishing the convergence proofs is demonstrated.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 15010118
• Report Number(s): PNNL-SA-35869
• Journal Information: Advances in Applied Mathematics, 29(2):311-327, Journal Name: Advances in Applied Mathematics, 29(2):311-327
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS