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YCor
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Spherical Harmonicharmonic expansion of a power function

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user4164
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Let $f$ be an even continuous function on the sphere $S^{n-1}$.

Find a relation of the spherical harmonic expansion of the functionbetween coefficients of $f^n$ and those of $f$.

Let $f$ be an even continuous function on the sphere $S^{n-1}$.

Find a spherical harmonic expansion of the function $f^n$.

Let $f$ be an even continuous function on the sphere $S^{n-1}$.

Find a relation of the spherical harmonic expansion between coefficients of $f^n$ and those of $f$.

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Spherical Harmonic expansion of a power function

Let $f$ be an even continuous function on the sphere $S^{n-1}$.

Find a spherical harmonic expansion of the function $f^n$.