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Ivan Izmestiev answered my question, see comments below.
In addition, the question above inspired me to find the explicit result for such integrals (they arise in the framework of weightedgeneralized Radon transforsmtransforms):
Ivan Izmestiev answered my question, see comments below.
In addition, the question above inspired me to find the explicit result for such integrals (they arise in the framework of generalized Radon transforms):