Difference between revisions of "Multiple series"
From Encyclopedia of Mathematics
(Importing text file) |
Ulf Rehmann (talk | contribs) m (tex encoded by computer) |
||
| Line 1: | Line 1: | ||
| − | + | <!-- | |
| + | m0654102.png | ||
| + | $#A+1 = 5 n = 0 | ||
| + | $#C+1 = 5 : ~/encyclopedia/old_files/data/M065/M.0605410 Multiple series, | ||
| + | Automatically converted into TeX, above some diagnostics. | ||
| + | Please remove this comment and the {{TEX|auto}} line below, | ||
| + | if TeX found to be correct. | ||
| + | --> | ||
| + | |||
| + | {{TEX|auto}} | ||
| + | {{TEX|done}} | ||
| + | |||
| + | '' $ s $- | ||
| + | tuple series'' | ||
An expression of the form | An expression of the form | ||
| − | + | $$ | |
| + | \sum _ {m,n \dots p = 1 } ^ \infty u _ {m, n \dots p } , | ||
| + | $$ | ||
| − | consisting of the terms from a table | + | consisting of the terms from a table $ \| u _ {m, n \dots p } \| $. |
| + | Each term of the table is indexed by $ s \geq 2 $ | ||
| + | indices $ m, n \dots p $, | ||
| + | which run independently of each other over the set of natural numbers. The theory of multiple series is analogous to the theory of [[Double series|double series]]. See also [[Absolutely convergent series|Absolutely convergent series]]. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> G.M. Fichtenholz, "Differential und Integralrechnung" , '''2''' , Deutsch. Verlag Wissenschaft. (1964)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> G.M. Fichtenholz, "Differential und Integralrechnung" , '''2''' , Deutsch. Verlag Wissenschaft. (1964)</TD></TR></table> | ||
Latest revision as of 08:02, 6 June 2020
$ s $-
tuple series
An expression of the form
$$ \sum _ {m,n \dots p = 1 } ^ \infty u _ {m, n \dots p } , $$
consisting of the terms from a table $ \| u _ {m, n \dots p } \| $. Each term of the table is indexed by $ s \geq 2 $ indices $ m, n \dots p $, which run independently of each other over the set of natural numbers. The theory of multiple series is analogous to the theory of double series. See also Absolutely convergent series.
References
| [1] | G.M. Fichtenholz, "Differential und Integralrechnung" , 2 , Deutsch. Verlag Wissenschaft. (1964) |
How to Cite This Entry:
Multiple series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiple_series&oldid=19098
Multiple series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiple_series&oldid=19098
This article was adapted from an original article by E.G. Sobolevskaya (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article