Abstract
In the solution of boundary value problems, usually zero eigenvalue is ignored. This case also happens in calculating the eigenvalues of matrices, so that we would often like to find the nonzero solutions of the linear systemAX=λXwhenλ≠0. Butλ=0implies thatdetA=0forX≠0and then the rank of matrixAis reduced at least one degree. This comment can similarly be stated for boundary value problems. In other words, if at least one of the eigens of equations related to the main problem is considered zero, then one of the solutions will be specified in advance. By using this note, first we study a class of special functions and then apply it for the potential, heat, and wave equations in spherical coordinate. In this way, some practical examples are also given.
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