Lauricella's Theorem

In the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely:

Theorem. A necessary and sufficient condition that a normal orthogonal set be closed is that the formal series for each function of a known closed normal orthogonal set in terms of converge in the mean to that function.

The theorem was proved by Giuseppe Lauricella in 1912.

Other articles related to "lauricella":

Lauricella Hypergeometric Series
... In 1893 Giuseppe Lauricella defined and studied four hypergeometric series FA, FB, FC, FD of three variables ... They are (Lauricella 1893) for

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