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Download fileOn Gegenbauer polynomials and coefficients clj(?) (1=j=l, ?>-1/2)
journal contribution
posted on 2023-06-09, 07:09 authored by Richard Olu Awonusika, Ali TaheriAli TaheriThe Gegenbauer coefficients cjl(?)(1=j=l, ?>-1/2) appear in the Maclaurin expansion of the heat kernels on the n-sphere and the real projective n-space. In this note we show that these coefficients can be computed by transforming the higher order derivative formula for the Gegenbauer polynomials Ck?(k=0,?>-1/2) into a spectral sum involving the powers of the eigenvalues of the associated Gegenbauer operator. We present explicit computations and various implications.
History
Publication status
- Published
File Version
- Accepted version
Journal
Results in MathematicsISSN
1422-6383Publisher
Springer VerlagExternal DOI
Issue
3Volume
72Page range
1359-1367Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes