New series involving harmonic numbers and squared central binomial coefficients
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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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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A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain fin...
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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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Motivated by recent works of Sun and Tauraso, we prove some variations on the Green-Krammer identity involving central q-binomial coefficients, such as n−1 ∑ k=0 (−1)kq−(k+1 2 ) [ 2k k ] q ≡ (n 5 ) q−bn 4/5c (mod Φn(q)), where ( n p ) is the Legendre symbol and Φn(q) is the nth cyclotomic polynomial. As consequences, we deduce that 3am−1 ∑
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2019
ISSN: 0035-7596
DOI: 10.1216/rmj-2019-49-8-2513