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

[ck99]

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.

 

[pwsnafu]

Riemann zeta.

 

[ck99]

Thankyou for the quick response, I can figure it out from that.

 

[Mute]

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)

 

[AlephZero]

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.

 

[ck99]

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!

 

[Michael Redei]

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?