q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev
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q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev Boris A KUPERSHMIDT The University of Tennessee Space Institute, Tullahoma, TN 37388, USA E-mail: [email protected] Received November 19, 2002; Accepted January 03, 2003 Abstract The sequence of period 6 starting with 1, 1, 0,−1,−1, 0 appears in many different disguises in mathematics. Various q-versions of this sequence are found, and their relations with Euler’s pentagonal numbers theorem and Chebyshev polynomials are discussed. The motto on Cardinal Newman’s tomb ought to be the funeral motto of every Catholic, Ex umbris et imaginibus in veritatem, Out of shadows and appearances into the truth. Ronald Knox, The Pastoral Sermons
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تاریخ انتشار 2003