Relations among spheroidal and spherical harmonics

R. García-Ancona, J. Morais and R. Michael Porter

Applied Mathematics and Computation, 2020, vol. 384, issue C

Abstract: A contragenic function in a domain Ω⊆R3 is a reduced-quaternion valued (i.e the last quaternionic coordinate is zero) harmonic function, which is orthogonal in L2(Ω) to all reduced-quaternion monogenic functions and their conjugates. Contragenicity is not a local property. For spheroidal domains of arbitrary eccentricity, we relate standard orthogonal bases of harmonic and contragenic functions for one spheroid to another via computational formulas. This permits us to show that there exist nontrivial contragenic functions common to the spheroids of all eccentricities.

Keywords: Spherical harmonics; Spheroidal harmonics; Quaternionic analysis; Monogenic function; Contragenic function (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320301168

DOI: 10.1016/j.amc.2020.125147

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