  We observe that the linearization coefficients for ultraspherical polynomials
are the orthogonality weights for Racah polynomials with special parameters.
Then it turns out that the linearization sum with such a Racah polynomial as
extra factor inserted, can also be evaluated. The corresponding Fourier--Racah
expansion is an addition type formula which is dual to the well-known addition
formula for ultraspherical polynomials. The limit to the case of Hermite
polynomials of this dual addition formula is also considered. Similar results
as for ultraspherical polynomials, although only formal, are given by taking
the Ruijsenaars--Halln\"as dual product formula for Gegenbauer functions as a
starting point and by working with Wilson polynomials.

Classical Analysis and ODEs