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The multi-indexed Laguerre and Jacobi polynomials form a complete set oforthogonal polynomials. They satisfy second-order differential equations butnot three term recurrence relations, because of the 'holes' in their degrees.The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressionsoriginating from multiple Darboux transformations. For the ease ofapplications, two different forms of simplified expressions of themulti-indexed Laguerre and Jacobi polynomials are derived based on variousidentities. The parity transformation property of the multi-indexed Jacobipolynomials is derived based on that of the Jacobi polynomial.

Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials