Abstract
An investigation of expansion problems in terms of spherical wave functions from different points of view is given. The possibility of having infinitely many formal series representations for a given function in terms of the associated Legendre functions <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p_{n}^{m}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sin \theta(dp_{n}^{m}/d\theta</tex> is also pointed out. One of the representations is derived by the use of the orthogonality relation, and the infinitely many others are derived by the use of the recurrence relation.
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