Power Series with Inverse Binomial Coefficients and Harmonic Numbers
نویسندگان
چکیده
منابع مشابه
Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers
We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences ( 2n n ) Hn, ( 2n n ) 1 nHn, ( 2n n ) 1 n+1Hn , and ( 2n n ) n m. The technique is based on a special Euler-type series transformation formula.
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Anthony Sofo Victoria University College, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia Correspondence should be addressed to Anthony Sofo, [email protected] Received 18 January 2011; Accepted 3 April 2011 Academic Editor: Toufik Mansour Copyright q 2011 Anthony Sofo. This is an open access article distributed under the Creative Commons Attribution License, which...
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We establish various generating functions for sequences associated with central binomial coefficients, Catalan numbers and harmonic numbers. In terms of these generating functions, we obtain a large variety of interesting series. Our approach is based on manipulating the well-known generating function of the Catalan numbers.
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ژورنال
عنوان ژورنال: Tatra Mountains Mathematical Publications
سال: 2017
ISSN: 1210-3195
DOI: 10.1515/tmmp-2017-0027