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Integral identities derived from the complex Funk-Hecke formula

In this paper we derive integral identities involving both the unit sphere and the unit disk or subsets thereof. In addition these identities lead to a prototype of the Funk-Hecke formula for subspheres embedded in $Ω_{2q}$. The technique requires the use of the complex Funk-Hecke formula, where eigenvalues of the integral operator generated by a bizonal kernel on the unit sphere $Ω_{2q}$ of $\mathbb{C}^q$ are given by an integral on the closed unit disk $B_q$ of $\mathbb{C}^{q-1}$.