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Excerpt from Infinite Determinants in the Theory of Mathieu's and Hill's Equations Finally, in Section II we prove the well-known theorem about the mutually exclusive nature of the four conditions using the infinite determinants This theorem is the negative aspect (in the case of Mathieu's equation) of the problem of finding equations of Hill's type (8) which have two linearly independent solutions of the same period. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.