Integer Part of the Partial Sums for the Divergent p-Series in Closed Form

2020 ◽  
Vol 127 (6) ◽  
pp. 554-557
Author(s):  
M. A. Nyblom
Keyword(s):  
Closed Form ◽  
Partial Sums ◽  
Integer Part

scholarly journals POWER SERIES WITH SKEW-HARMONIC NUMBERS, DILOGARITHMS, AND DOUBLE INTEGRALS

2013 ◽  
Vol 56 (1) ◽  
pp. 93-108
Author(s):  
Khristo N. Boyadzhiev
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Harmonic Series ◽  
Partial Sums ◽  
Simultaneous Solution ◽  
College Mathematics ◽  
Harmonic Numbers ◽  
Numerical Series ◽  
Double Integrals

ABSTRACT The skew-harmonic numbers are the partial sums of the alternating harmonic series, i.e., the expansion of log 2.We evaluate in closed form various power series and numerical series with skew-harmonic numbers. This provides a simultaneous solution of two recent problems by Ovidiu Furdui in the American Mathematical Monthly and the College Mathematics Journal. We also present and discuss representations involving the dilogarithm and the trilogarithm which are related to our results. Finally, we provide the evaluations of several double integrals in terms of classical constants.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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