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Abstract
This paper gives a brief exposition of several recent results obtained by the authors concerning some classes of inverse relations, including the general binomial-type inversions and two kinds of general Stirling reciprocal transforms. Also described are some applications of the related inversion techniques to combinatorics (including new proofs of Rogers-Ramanujan identities and MacMahon's master theorem), interpolation methods and certain problems related to special polynomials and number sequences.
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