What does the word-final sigma symbol mean in maths?

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Discussion Overview

The discussion revolves around the meaning of the "word-final" sigma symbol in mathematics, specifically in relation to its appearance and usage in Greek letters. Participants explore the distinction between sigma and zeta, as well as the context in which these symbols are used, particularly in mathematical notation and typesetting with LaTeX.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the "word-final" version of sigma, which they believe resembles ζ, and expresses a need for a definition to evaluate 3ζ(4).
  • Another participant identifies the symbol as the Riemann zeta function, ζ.
  • A later reply questions the term "word-final" and suggests that the participant may be referring to varsigma (##\varsigma##), which is a variation of sigma used in specific contexts.
  • It is noted that the letter ζ is actually 'zeta', and varsigma and zeta, while similar, are different symbols.
  • One participant mentions that the term "varsigma" was coined by Knuth for TeX, and that it is rarely used in mathematical contexts.
  • Another participant expresses confusion between sigma and zeta after reviewing a list of Greek symbols.
  • There is a discussion about the ease of writing Greek text in LaTeX, with one participant explaining that LaTeX automatically adjusts the shape of sigma based on its position in a word.

Areas of Agreement / Disagreement

Participants generally agree on the distinction between sigma and zeta, but there is some confusion regarding the terminology and the use of varsigma. The discussion remains unresolved regarding the specific use of "word-final" sigma and its implications in mathematical notation.

Contextual Notes

There is a lack of consensus on the terminology used to describe the different forms of sigma and their applications in mathematics and typesetting. Some assumptions about the familiarity with Greek symbols and LaTeX may not hold for all participants.

ck99
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Hi all, I have spent a good half hour searching for the meaning of this, but have only found results for upper-case sigma Ʃ and lower-case sigma σ. Can anyone tell me the meaning of the "word-final" version of sigma, which looks like ζ ?

I am trying to evaluate 3ζ(4) but I just need a definition or something to get me started!

Thanks.
 
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Thankyou for the quick response, I can figure it out from that.
 
ck99 said:
Hi all, I have spent a good half hour searching for the meaning of this, but have only found results for upper-case sigma Ʃ and lower-case sigma σ. Can anyone tell me the meaning of the "word-final" version of sigma, which looks like ζ ?

I am trying to evaluate 3ζ(4) but I just need a definition or something to get me started!

Thanks.

I'm curious, what do you mean by ' "word-final" version of sigma '? Is 'word-final' a program, and are you referring to ##\varsigma##, a variation of ##\sigma## (usually called, appropriately, 'varsigma')?

The letter you have actually written, ##\zeta##, is 'zeta'. ##\varsigma## and ##\zeta##, though very similar, are different. (Almost no one actually uses ##\varsigma## to denote anything, it's pretty rare)
 
Mute said:
I'm curious, what do you mean by ' "word-final" version of sigma '? Is 'word-final' a program, and are you referring to ##\varsigma##, a variation of ##\sigma## (usually called, appropriately, 'varsigma')?

I think Knuth invented the name "varsigma" for TeX (and also varpi, vartheta, etc). AFAIK Greeks just call it "sigma", and it happens to be written with a different shape when it is the last letter of a Greek word. (There doesn't have to be a reason why. It just is.)

I don't think "varsigma" is ever used as a math symbol. Knuth created it so you could write Greek text in TeX.

But if you want to write Greek text in LaTeX, you don't need to bother with that low level stuff, you just tell Latex you want to write Greek, type "s" and you get the right version of sigma automatically.

FWIW other scripts (e.g. Hebrew and Arabic) have many letters that have different shapes depending on their position within a word. Some Arabic letters have four different shapes, not just two like Greek sigma.
 
You're right, I think I was getting confused between sigma and zeta. I just looked at a list of greek symbols and tried to find the one with the best match!
 
AlephZero said:
But if you want to write Greek text in LaTeX, you don't need to bother with that low level stuff, you just tell Latex you want to write Greek, type "s" and you get the right version of sigma automatically.

Wow, I didn't realize it was that easy, although I've been using LaTeX for quite some time. How do I "just tell" LaTeX that I want to write Greek? Surely there's some style file I need to use and some special font that needs to be installed?
 

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