On the Green function to the biharmonic equation on n -dimensional sphere

Key Points

• The aim is to explore the Green function for both homogeneous and inhomogeneous biharmonic equations on the n-dimensional unit sphere.
• Consideration of the biharmonic equation on the n-dimensional unit sphere
• Representation of the Green function as a series of Gegenbauer polynomials
• Derivation of explicit forms for various parameter sets
• The Green function is expressed as a series of Gegenbauer polynomials, allowing for a detailed analysis.
• Explicit representations of the Green function were determined for specific parameter sets, expanding on existing mathematical theories.