Dilution of a series
From Encyclopedia of Mathematics
The inclusion of any finite number of zeros between adjacent terms of a series. For the series
 | (*) |
a diluted series has the form
 |
Dilution of a series does not affect convergence of the series, but it may violate summability of the series (after dilution a series (*) summable to the number 
by some summation method may turn out to be not summable at all by this method or may turn out to be summable to a number 
).
How to Cite This Entry:
Dilution of a series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dilution_of_a_series&oldid=30623
Dilution of a series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dilution_of_a_series&oldid=30623
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article