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We study the following problem: given a regular symmetric form (linear functional)  v , find all the regular symmetric forms  u  which satisfy the equation. We give the second-order recurrence relation of the orthogonal polynomial sequence with respect to  u . Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.

Division problem of a regular symmetric form the case x 3 u = λ xv