[math-fun] product_{0<k<n, (k,n)=1} Gamma(z+k/n) ? [Was: product_{(k,n)=1} Γ(z+k/n) ?]
wds> Gosper has an annoying habit of using non-ASCII characters I cannot read, which come out as "?" on my screen. Or maybe they really are "?". Who knows? hmm, that might explain why I'm not getting any answers. Off list I've been merrily exchanging emails with Chinese and all sorts of exotica from the Special Characters menu. But this time the culprit is not math-fun--I can see the Uppercase Gamma in my Subject summary window, where there's a ? in Warren's reply. Who else is having this problem? Was anybody besides Warren pwned by my BLACK RIGHT-POINTING SMALL TRIANGLE (▸), (which GMail has suddenly stopped inserting on double-clicking the font table)? Maybe Warren is alone on a network made of juice cans and string? Anyway, he's right. I should've stipulated 0<k<n under the product. But he might have guessed my intent from the n=12 example, which is plain ASCII, except for the pi. Haven't we been using π quite a while now? It's just option p on the Mac keyboard. --rwg On Fri, Jan 18, 2013 at 3:39 PM, Bill Gosper <billgosper@gmail.com> wrote:
Someone once sent me (us?) a paper deriving (presumably by inclusion-exclusion) this gamma product formula. Does anyone remember where it is? Presumably for n=12 it gives something like
(z - 11/12)!*(z - 7/12)!*(z - 5/12)!*(z - 1/12)!== 4*(2*z)!*(12*z)!*π^2/(2^(12*z)*3^(6*z)*(4*z)!*(6*z)!)
It doesn't seem to be on http://functions.wolfram.com/ --rwg
* Bill Gosper <billgosper@gmail.com> [Jan 19. 2013 17:39]:
wds>
[...]
(I am aware that these email/format discussions are not exactly welcome on this list). I do recall that a had to change my terminal font (I use xterm) to be able to see all of the UTF-8 characters. Guessing that Warren uses mutt as MTA as I do (the MTA of annoying people, har, har), he may just just have to do that.
From my .Xresources: xterm*font: -b&h-lucidatypewriter-medium-r-normal-sans-12-120-75-75-m-70-iso10646-1
(I seem to recall the iso10646 being crucial) Here's Greek (3 lines), Cyrillic (4 lines), and IPA (3 lines) as a test case: ------------------------------------------------------------ Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ ς Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω Cyrillic: А а Б б В в Г г Ґ ґ Ѓ ѓ Д д Ђ ђ Е е Ё ё Є є Ж ж З з Ѕ ѕ И и І і Ї ї Й й Ј ј К к Ќ ќ Л л Љ љ М м Н н Њ њ О о П п Р р С с Т т Ћ ћ У у Ў ў Ф ф Х х Ц ц Ч ч Џ џ Ш ш Щ щ Ъ ъ Ы ы Ь ь Э э Ю ю Я я ́ IPA: t̪ d̪ ʈ ɖ ɟ ɡ ɢ ʡ ʔ ɸ ʃ ʒ ɕ ʑ ʂ ʐ ʝ ɣ ʁ ʕ ʜ ʢ ɦ ɱ ɳ ɲ ŋ ɴ ʋ ɹ ɻ ɰ ʙ ʀ ɾ ɽ ɫ ɬ ɮ ɺ ɭ ʎ ʟ ɥ ʍ ɧ ɓ ɗ ʄ ɠ ʛ ʘ ǀ ǃ ǂ ǁ ɨ ʉ ɯ ɪ ʏ ʊ ɘ ɵ ɤ ə ɚ ɛ ɜ ɝ ɞ ʌ ɔ ɐ ɶ ɑ ɒ ʰ ʷ ʲ ˠ ˤ ⁿ ˡ ˈ ˌ ː ˑ ̪ ------------------------------------------------------------ cheers, jj
On 1/19/13, Bill Gosper <billgosper@gmail.com> wrote:
Who else is having this problem? Was anybody besides Warren pwned by my BLACK RIGHT-POINTING SMALL TRIANGLE (▸), (which GMail has suddenly stopped inserting on double-clicking the font table)?
Maybe Warren is alone on a network made of juice cans and string?
Not in this instance --- I'm using an 8-year old Mac, and every so often Bill's utterances do arrive peppered with query marks. On this occasion however, his BLACK RIGHT-POINTING SMALL TRIANGLE prints as intended! Incidentally, Warren's mailer manages to corrupt the subject cryptically, disconnecting his reply from the preceding Gmail thread, despite subject line remaining apparently unaltered. Those inhabiting glasshouses ... WFL
"BG" == Bill Gosper <billgosper@gmail.com> writes:
BG> Who else is having this problem? Your email comes from the list as text/plain charset=utf-8. There is no excuse for any currently-maintained email software to be unable to handle that, though one does need to have enough fonts (either just available or explicitly configured, depending on the software) to cover the characters used. Given that you both seem to use gmail, that he cannot see what you wrote suggests either a browser issue or that he uses gmail via imap or pop3 with archaic software. -JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 1024D/ED7DAEA6
When you leave the ascii domain, what you see is only vaguely related to what you send, and what you send is only vaguely related to what the recipient sees. There are many possible levels of encoding and many possibilities for the display of the decoded information. For example, your recent subject line displays approximately like this on my email system, which I wrote to deliberately limit subject lines to plain ascii: Subject: [math-fun] iso-8859-7?b?cHJvZHVjdF97MDxrPG4sIChrLG4pPTF9IEdh?= iso-8859-7?b?bW1hKHoray9uKSA/IFtXYXM6IHByb2R1Y3RfeyhrLG4pPTF9?= iso-8859-7?b?IMMoeitrL24pID9d?= (some characters were removed to inhibit multibyte character interpretation). Also, the spam evaluation done by my ISP's software is mildly prone to calling you a miscreant: * 1.5 TR_Symld_Words too many words that have symbols inside * 0.1 XMSubLong Long Subject * 0.0 HTML_MESSAGE BODY: HTML included in message * 0.8 BAYES_50 BODY: Bayes spam probability is 40 to 60% * [score: 0.5000] * 0.0 T_TooManySym_04 7+ unique symbols in subject * 0.0 T_TooManySym_01 4+ unique symbols in subject * 0.0 T_TooManySym_05 8+ unique symbols in subject * 0.0 T_TooManySym_03 6+ unique symbols in subject * 0.0 T_TooManySym_02 5+ unique symbols in subject Hilarie
="Bill Gosper" <billgosper@gmail.com>
=wds>
Gosper has an annoying habit of using non-ASCII characters I cannot
read, which come out as "?" on my screen. Or maybe they really are "?".
Maybe Warren is alone on a network made of juice cans and string? Alas he's not alone; the entire Internet is made of juice cans and string.
plain ASCII, except for the pi. Haven't we been using ¼ quite a while now? It's just option p on the Mac keyboard.
"Just". As it happens, for work I have recently been dealing with a swarm of pesky bugs with the handling of non-ASCII characters. In complex heterogeneous webs of systems the quantity and variety of crazy things that can and will go wrong is astonishing. For example different computers along a dataflow get configured to use subtly different coding and escaping standards ("a good thing about standards being there's so many to choose from"). For example I've seen a forms where every time you simply refresh your browser each non-ASCII character in your input box gets rewritten into a cluster of ever-more random non-ASCII characters, like some sort of malignant symbolic LIFE mutation. And then some poor users then actually hit the button to submit the form (it being too late for HTTP POST's "official" idempotency to help). So if you are conversing within a work group or something where you know everybody is using identical systems (say all Gmail on Macs or whatever) then you might go ahead and include non-ASCII. But if there's the slightest diversity (eg as with math-fun) garble is almost inevitable, and you should hew to truly plain-spoken ASCII if you want to avoid it. Alas even that's not always easy--ubiquitous know-it-all software is ever ready to molest innocent text with spell-"correction", "smart" quotes and other clever misfeatures. Just a few days ago another list I'm on actually sent out a test message with eleven variant strings in order to experimentally determine just how badly "autoformat" was mangling their threads. What year is this? 2013? I think we now have sufficient evidence: "The idiocy of the computing experience roughly doubles every 18 months."
participants (6)
-
Bill Gosper -
Fred lunnon -
Hilarie Orman -
James Cloos -
Joerg Arndt -
Marc LeBrun